## Achievement First Mathematics

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###### Usability
Our Review Process

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### Overall Summary

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

### Focus & Coherence

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. Above-grade-level assessment questions are present but could be modified or omitted without a significant impact on the underlying structure of the materials.

The series is divided into nine units, and each unit contains a Unit Assessment available online in the Unit Overview document and can also be printed for students. Unit Assessments contain suggestions for use of Post-Unit Assessment questions as Pre-Unit Assessment questions. Teachers are directed to adjust instruction according to the Pre-Assessment results. Some parts of the assessment may be read to the students or done orally in small groups.

Examples of assessment questions aligned to grade-level standards include:

• Unit 2, Geometry Unit Assessment, Question 2, “Cross out the shapes that have 4 corners.” Pictures of a variety of two-dimensional shapes are given. (1.G.1)

• Unit 3, Story Problems 1 Unit Assessment, Question 1, “Maya had 3 books. Sean had 5 books. How many books did they all have?” (1.OA.1)

• Unit 5, Addition & Subtraction Unit Assessment, Question 5, “a. Sally had 4 stickers in her sticker collection. Her teacher gave her some more. Now she has 12. How many stickers did her teacher give her? b. What subtraction problem could you use to solve this story problem?” (1.OA.6)

• Unit 6, Two-Digit Numbers 1 Unit Assessment, Question 2, “Shanaya had 47 cubes. How many towers of ten could she make and how many single cubes would be left over?” (1.NBT.2)

• Unit 8, Measurement Unit Assessment, Question 1, “Which shows the flowers in order from shortest to tallest?” The item is followed by four choices, each displaying three flowers in different order by height. (1.MD.1)

There are examples of above-grade-level assessment questions. The Guide to Implementing AF Math: Grade 1 and the assessments do not consistently align questions to the same standards. The Guide to Implementing AF Math: Grade 1, “Teachers should remove these items or use them for extension purposes only.” For example:

• Unit 8, Measurement Unit Assessment, Question 4, “Steven’s foot is two inches shorter than Jason’s foot. Jason’s foot is 7 inches long. How long is Steven’s foot?” According to the Guide for Implementing AF Math: Grade 1, “Problems 4, 9, and 10 align with standard 2.MD.5.”

• Unit 8, Measurement Unit Assessment, Question 9, “Trout keepers are 10 inches long. Kim caught a trout that was 7 inches long. How much longer would her trout need to be to be a keeper?” According to the Guide for Implementing AF Math: Grade 1, “Problems 4, 9, and 10 align with standard 2.MD.5.”

• Unit 8, Measurement Unit Assessment, Question 10, “Julie’s bike is longer than Dave’s bike. Sarah’s bike is shorter than Dave’s bike. Whose bike is longer Julie’s or Sarah’s?” According to the Guide for Implementing AF Math: Grade 1, “Problems 4, 9, and 10 align with standard 2.MD.5.”

• Unit 9, Two-Digit Numbers 2 Unit Assessment, Question 7, “67-22.” In Grade 1, students subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (1.NBT.6). This question aligns to 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction).

• Unit 9, Two-Digit Numbers 2 Unit Assessment, Question 8, “88-54.” In Grade 1, students subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 (1.NBT.6). This question aligns to 2.NBT.5 (Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction).

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Each unit consists of lessons that are broken into four components: Introduction, Workshop/ Discussion, Independent Practice, and Exit Ticket. In addition to lessons, there are Math Stories “to enable students to make connections, identify and practice representation and calculation strategies, and develop deep conceptual understanding through the introduction of a specific story problem type in a clear and focused fashion with deliberate questioning and independent work time,” and Math Practice (Practice Workbook) for students “to build procedural skill and fluency.” Examples include:

• Unit 2, Lesson 3, Exit Slip, students engage with 1.G.1 as they build and draw shapes that possess defining attributes. Students experience the full intent of 1.G.1 as they draw three-sided shapes with defining attributes. “Rule: Shapes with exactly 3 corners. In the shape draw a circle that meets the rule. Outside the circle, draw a shape that does not meet the rule.”

• Unit 6, Lesson 17, Workshop, students engage with 1.NBT.5 as they are given a two-digit number and asked to mentally find 10 more or 10 less than the number, without having to count and explain the reasoning used. Students practice the skill of mentally finding 10 more or 10 less through a card game of Leapfrog. Students roll dice telling them how many spaces to move forward on a game board, then draw a card telling them how many tens to leap ahead. The Workshop includes Check for Understanding questions such as “How did you solve? Why? Why does that work?” The full intent of the standard is met as students explain their reasoning. In the Exit Ticket, Problem 2, “Solve. 58 + 30 = ______.”

• Unit 8, Lesson 7, students engage with 1.MD.1 as they order three objects by length and compare the lengths of two objects indirectly by using a third object. Students are provided with extensive work with this standard including five problems during Workshop, two problems within Practice Workbook D and eight problems within the Exit Tickets. Exit Ticket, “On the lines below, write the names of the objects in order from shortest to longest.” Students are shown images of a cup, a sneaker, and a ball.

• Unit 5, Lessons 18-23, students engage with 1.OA.7 to understand the meaning of the equal sign and determine if equations involving addition and subtraction are true or false. There are six lessons addressing this standard. As a result, the full intent of the standard is met for all students. The lessons focus on students matching expressions that are equal, asking the question “are they the same amount?”, determining if an equation is true or false by asking “are both sides of the equal sign the same value, by creating true equations using what they know about the equal sign, and revising false equations to make them true. In Lesson 20, Introduce the Math, “Yesterday we learned what the word equal means. What does equal mean? (Equal means the same.) In math, we have a special symbol to show that two amounts are equal. Raise your hand if you know what it is. (The equal sign.)...Today, we will learn more about the equal sign and how it works in equations by playing a game called True or False Sort. In this game, you will see lots of equations...Some will be true and some will be false like the one we just saw. It’s our job to figure out which is which.”

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

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When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

• The approximate number of units devoted to major work of the grade, including assessments and supporting work connected to the major work, is 6.5 out of 9, which is approximately 72%.

• The number of lessons devoted to major work of the grade, including assessments and supporting work connected to the major work, is approximately 113 out of 150, which is approximately 75%.

• The instructional block includes a math lesson, math stories, and math practice components. The non-major component minutes were deducted from the total instructional minutes resulting in 9,200 major work minutes out of 12,750 total instructional minutes. As a result of dividing the major work minutes by the total minutes, approximately 72% of the materials focus on major work of the grade.

A minute-level analysis is most representative of the materials because the minutes consider all components included during math instructional time. As a result, approximately 72% of the materials focus on major work of the grade.

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Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The publishers identify connections between supporting content and major work within the lesson plan in the “Standards in Lesson” section, as well as in the Guide to Implementing AF Math: Grade 1. Additional connections exist within the materials, although not always stated by the publisher. In addition, the publisher identifies the CCSSM clusters at the top of each lesson plan as the “CC Clusters in Unit.” However, the major clusters listed are not consistent throughout the unit, and, therefore, it is unclear how the publisher identified clusters connected to the unit. For example, in Unit 5, Lesson 7, the publisher identifies 1.OA.A, represent and solve problems involving addition and subtraction, as connected to Unit 5. However, the 1.OA.A standards are not identified in any Unit 5 lesson. Examples of the connections between supporting work and major work includE:

• Unit 2, Lesson 7, Exit Ticket, students engage with the supporting work of 1.G.2, compose two-dimensional shapes or three-dimensional shapes to create a composite shape and the major work of 1.OA.1, use addition and subtraction within 20 to solve word problems by having students determine how to use the fewest pattern block shapes to fill a larger shape, complete a table, and add to find the total number of shapes used. Problem 2, “Elijah is trying to figure out a way to fill the same pattern using more than 4 pattern blocks. What is a way that he can fill the shape that uses more than 4 pattern blocks? Fill in the table to show how you fill the shape.” The table provided includes pictures of the different pattern blocks available, a place to record the number used, and a place to provide the total number of blocks used.

• Unit 4, Lesson 4, Exit Ticket, students engage with the supporting work of 1.MD.4, interpret data with up to three categories and answer questions about the total number of data points. This lesson also addresses, although not stated, the major work of 1.OA.2, adding three whole numbers whose sum is less than or equal to 20. A bar graph is shown representing the favorite sport of 3rd graders. Problem 3, “How many kids took the survey?”

• Unit 7, Lesson 6, Exit Ticket, students engage with the supporting work of 1.MD.3, tell and write time in hours and half-hours and with the major work of 1.NBT.1, read and write numbers to 120. In this lesson, students tell and write time in hours and half-hours using analog and digital clocks. In Problem 1, students are shown a digital clock showing 10:30 as the time. They are given a clock face without hands on it and asked to, “Draw the hands to show the time.”

• Practice Workbook E, students engage with the supporting work of 1.MD.4, interpreting data up to three categories, and the major work of 1.OA.2, solving word problems that call for addition of three whole numbers whose sum is less than or equal to 20. 1.MD.4 is the only standard identified for this problem. In Problem 2, students are presented with a table that shows the types of shoe ties with three categories: “velcro, laces, no ties.” Students are asked, “Write a number sentence to show how many total students are asked about their shoes.”

##### Indicator {{'1e' | indicatorName}}

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.  Examples of connections include:

• Unit 3, Lesson 7, Exit Ticket, students engage with 1.OA.B, understand and apply properties of operations and the relationship between addition and subtraction, and 1.OA.C, add and subtract within 20, as they are provided different strategy options to solve and write an addition equation. Problem 1, “Solve for the unknown. Write an addition equation that shows the parts and whole (You may use the number line but do not have to.)” Students are provided with a number bond with 8 and 5 in two of the circles, a space to write the addition equation, and a number line to use.

• Unit 5, Lesson 18, Workshop, students engage with 1.OA.B, understand and apply the properties of operations and the relationship between addition and subtraction, 1.OA.C, add and subtract within 20, and 1.OA.D, work with addition and subtraction equations. During Workshop, students play a game called “True Match” in which they use the strategies explored in recent lessons to solve efficiently. They have two sets of cards with equivalent matches and are to use the following strategies: solve for the total by counting on, solve for the total by making ten, just know the total, and just know the equivalent expression without solving either expression (compensating).

• Unit 6, Lesson 5, Workshop, students engage with 1.NBT.B, understand place value, and 1.NBT.A, extend the counting sequence, as they draw numbers 10-90 using sticks and dots and write the numeral. Exit Ticket, Problem 2, “If you have 4 tens and 2 ones, how many do you have? Represent with sticks and dots and write the numeral.”

• Unit 7, Lesson 5, Worksheet Packets engage students with 1.MD.B, tell and write time, and 1.G.A, reason with shapes and their attributes, as they identify a clock with a given time. Problem 1, “Circle the correct clock. 1. Half past 10 o’clock.” Students are provided with three clocks (10:30, 11:30, and 12:30).

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Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The Unit Overview supports the progression of First Grade standards by explicitly stating connections between prior grades and current grade level work. Each Unit Overview contains an Identify the Narrative component that identifies connections to what students learned before this First Grade unit and/or concepts previously learned in Kindergarten.

Each Unit Overview also contains an Identify Desired Results: Identify the Standards section that makes connections to supporting standards learned prior to the unit. In addition, some lessons make connections to previous grade-level learning in the Narrative section. Examples include:

• Unit 1, Lesson 2, Narrative, What is new and/or hard about the lesson?, “Students will be familiar with counting by tens and ones from kindergarten, and many will recall that it is useful to group objects into sets of tens and ones from their work with teen numbers.”

• Unit 2, Geometry Unit Overview, Identify the Narrative, “Throughout the unit, students identify the defining characteristics, or attributes, of two- and three-dimensional shapes, building on their Kindergarten experiences of sorting, analyzing, comparing, and creating various two- and three-dimensional shapes and objects (1.G.1).”

• Unit 3, Story Problems Unit Overview, Identify Desired Results, “K.OA.1 Represent addition and subtraction with objects, fingers, mental images, drawings (no detail), sounds (e.g., claps), acting out situations, verbal explanations, expressions, or equations,” and “K.OA.5 Fluently add and subtract within 5” as previous grade level standards related to “1.OA.1 Use addition and subtraction within 20 to solve world problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using objects, drawings, and equations with a symbol of the unknown number to represent the problem.”

• Unit 5, Addition and Subtraction Unit Overview, Identify the Narrative, “Make 10 is a valuable strategy in the base-ten system because it allows students to work flexibly with numbers to solve more challenging problems by breaking them down into easier problems that they can solve fluently. The building blocks for the make ten strategy are built in Kindergarten, as students become familiar with number partners for numbers 1-10, decompose teen numbers into a group of ten and some more ones. If students are struggling to use the make ten strategy, teachers should ensure that the students solidly understand K.OA.4, K.OA.3, and K.NBT.1 because they are foundational for the make ten strategy.”

• Unit 8, Measurement Unit Overview, Identify Desired Results: Identify the Standards, 1.MD.2 (Express the length of an object as a whole number of length unit, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.) is identified as a Unit 8 standard. The Kindergarten standard identified as foundational is K.MD.1 (Describe measurable attributes of objects, such as length or weight. Describe several measurable attributes of a single object.)

The Unit Overview documents contain an Identify the Narrative component that looks ahead to content taught in future grades. In addition, the Linking section includes connections taught in future grades, units, or lessons. Evidence of prior and future grade-level work supporting the progressions in the standards is identified. Examples include:

• Unit 1, Counting Unit Overview, Identify the Narrative, Linking, “Continuing through the rest of elementary school, students will use the counting sequence in all grades. In 2nd grade they’ll be using the counting and place value patterns to count to 1,000 and add and subtract within 1,000. This becomes fluent in 3rd grade. By fourth grade, they’ve generalized the counting and place value patterns to all numbers and can add and subtract any size and number.”

• Unit 3, Story Problems Unit Overview, Identify The Narrative, Linking, “In the rest of elementary school, students will continue to work with story problems following the protocol taught and practiced in this unit. In second grade, students will master the start unknown, compare-bigger unknown-fewer, and compare-smaller unknown-more problem types that they were exposed to in this unit, and they will begin to solve two-step story problems. They will continue to expand their bank of representation and solution strategies.”

• Unit 5, Addition and Subtraction Unit Overview, Identify the Narrative, Linking, “Looking ahead to the remainder of first grade, students will continue to use the strategies taught in this unit to efficiently solve addition and subtraction problems and story problems within 20. They will build on these strategies to solve problems beyond 20 and up to 100, especially using count on and count back to add and subtract multiples of 10 to two-digit numbers.”

• Unit 8, Measurement Unit Overview, Identify The Narrative, Linking, “In the remainder of first grade, comparing lengths of objects help support students in understanding and solving compare-difference unknown story problems. Moving into second grade, students begin to use standard units of measurements such as rulers, yardsticks, meter sticks, and measuring tapes to measure and estimate length. They relate the length of a unit of measurement to the length of the object being measured with that unit. (For example, students recognize that a table would be more inches long than feet because inches are shorter than feet.) Second graders also build on the compare work they did in first grade to determine how much longer one object is than another, expressing the difference in terms of a standard length unit.”

• Unit 9, Two Digit Numbers 2 Unit Overview, Identify the Narrative, Structural Overview outlines the concepts of addition and subtraction across grades K to 4. The visual shows that addition and subtraction within 10 occurs in Kindergarten, while within 100 occurs in First Grade and within 1,000 occurs in Second through Fourth Grades. It also identifies that Properties of Addition and Subtraction are learned from First Grade through to Fourth Grade, while the Standard Algorithm for addition and subtraction is taught in Fourth Grade.

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In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The instructional materials reviewed for Achievement First Mathematics Grade 1 foster coherence between grades and can be completed within a regular school year with little to no modification.

The Guide to Implementing AF, Grade 1 includes a scope and sequence. “Not every lesson is entirely focused on grade level standards, and, therefore, some lessons can be used for either remediation or enrichment.” As designed, the instructional materials can be completed in 150 days. One day is provided for each lesson and one day is allotted for each unit assessment.

• Nine units with 141 lessons in total.

• The Guide identifies lessons as either R (remediation), O (on grade level), or E (enrichment).  There are 10 lessons identified as E (enrichment), 0 identified as R (remediation), and 131 identified as O (on grade level).

• Nine days for unit assessments.

When reviewing the materials for Achievement First, Grade 1, a difference in the number of total instructional days was found. Although the publisher states the curriculum will encompass 151 days, there are 150 days of lessons and unit assessments.  The Grade 1 Unit Overview for Unit 6 shows 24 days for the unit while the Guide to Implementing AF, Grade 1 provides 23 days for the unit. The unit has 23 lessons including the unit assessment.

The publisher recommends 85 minutes of mathematics instruction daily.

• There are two lesson types, Game Introduction Lesson or Task Based Lesson. Each lesson is designed for 45 minutes.

• Math stories are designed for 25 minutes.

• Calendar/practice is designed for 15 minutes.

### Rigor & the Mathematical Practices

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for rigor and balance and practice-content connections. The materials reflect the balances in the Standards and help students develop conceptual understanding, procedural skill and fluency, and application. The materials make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor and Balance

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications of mathematics, and do not always treat the three aspects of rigor together or separately.

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Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Achievement First Mathematics Grade 1 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

Materials include problems and questions that develop conceptual understanding throughout the grade-level. Examples include:

• Unit 3, Lesson 5, Introduction, students engage with 1.OA.3, apply properties of operations as strategies to add and subtract, 1.OA.4, understand subtraction as an unknown-addend problem, and 1.OA.5, relate counting to addition and subtraction, as they represent addition and subtraction scenarios with number bonds. The teacher models how to play Roll and Record: Mixed Operations. “Step 1: Pick a card and roll 2 cubes. (pick addition operation card first - for planning purposes, assume you roll 4 and 6), Step 2: solve and record equation. What’s the total?, Step 3 says record with a number bond; label parts and whole, Step 4 says record with other operation equation. We already wrote an addition equation… so now we need to record with subtraction.”

• Unit 5, Lesson 6, Introduction, students engage with K.CC.6, identify whether the number of objects in one group is greater than, less than, or equal to the number of objects in another group, as they play a game called Compare. During the Introduction, two cards are drawn (example, 7 and 9) and students are asked to pictorially show which is more or less by drawing circles on their whiteboards. The teacher asks, “How do you know from the picture?” A sample student response might be, “I know because in the picture you can see that there are extra circles in the row of 9 and the row of 7 is missing some.”

• Unit 6, Lesson 2, Workshop, students engage with 1.NBT.2, understand that the two digits of a two-digit number represent amounts of tens and ones, as they select a bag with 10-90 cubes and draw a representation of the two-digit numbers, showing tens and ones. The teacher is provided support in the Assessment and Criteria for Success portion of the lesson, “Students will pick a bag that is filled with ten sticks and loose ones. They will determine how many by counting by tens and ones and draw a literal picture and write a numeral to match. Students should be able to explain why they are counting by tens and ones and what their picture and numeral represents. For example, ‘In my picture I drew 7 ten sticks and can count them by ten because there are ten cubes in each stick. Then I draw 4 loose ones and I would count on by ones. So “10, 20, 30, 40, 50, 60, 70, 71, 72, 73, 74.” There are 74. I would write 7 to show 7 groups of ten and 4 to show 4 loose ones.’”

• Unit 6, Lesson 20, Introduction, students engage with 1.NBT.3, by comparing two two-digit numbers based on the meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, <. Step 5, “Is 65 greater or less than 63? How can we figure it out? Strategy 1: Sticks and dots (intervention). SMS: We could look at the sticks and dots and it looks like 65 has the same number of sticks/tens as 63 but 65 has more ones than 63. Therefore, 65 is greater than 63.”

• Unit 9, Lesson 12, Workshop Worksheet, students engage with 1.NBT.6, subtract multiples of 10 in the range 10-90, using models, drawings, and strategies based on place value, as they subtract multiples of 10 from a two-digit number using strategies that work for them. Problem 4, “$$50 - 30 =$$ _____. How did you solve?”

Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

• Unit 3, Lesson 11, Exit Ticket, students engage with 1.OA.1, use addition and subtraction within 20 to solve word problems, as they solve story problems by visualizing and representing in a way that makes sense to them. Problem 2, “Tony was collecting buttons. He had 4 buttons and then his grandmother gave him 3 more buttons. How many buttons does he have now?”

• Unit 6, Lesson 9, Exit Ticket, students engage with 1.NBT.4, add within 100, including adding a two-digit number and a one-digit number and adding a two-digit number and a multiple of ten, as they combine two multiples of ten by using a strategy that makes sense to them (cubes, literal pictures, sticks and dots, count all/on by tens, use place value). Problem 1, “Solve. 30 + 20 = ____.”

• Unit 7, Practice Workbook D, students engage with 1.NBT.2, by understanding that the two digits of a two-digit number represent amounts of tens and ones. Problem 12, “Show the number 39 in tens and ones.”

• Unit 7, Practice Workbook D, students engage with 1.NBT.6, subtract multiples of 10 in the range 10-90, using models, drawings, and strategies based on place value, as they independently subtract multiples of 10 from a two digit number using strategies that work for them. Problem 1, “$$80 - 60 =$$ _______.”

• Unit 9, Lesson 12, Exit Ticket, students engage with 1.NBT.6, subtract multiples of 10 in the range 10-90 from multiples of 10 in the range of 10-90, as they use strategies that work for them (count what’s left, count back, uses known facts). Problem 1, “Solve. 50 - 30 = __.” Additional guidance for the teacher is found in Assessment and Criteria for Success, “Students should be able to describe their work by saying, ‘I solved 50 - 30. First I drew 5 sticks and 0 dots to show 50 because there are 5 tens and 0 ones. Then I need to take away 30, which is 3 tens and 0 ones. So as I crossed out the sticks I counted back like this. 50 -- 40, 30, 20. The difference is 20.’”

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Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials for Achievement First Mathematics Grade 1 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.These skills are delivered throughout the materials in the use of games, workshop, practice workbook pages and independent practice, such as exit tickets.

The materials develop procedural skill and fluency throughout the grade level. Examples include but are not limited to:

• Unit 3, Lesson 9, Assessment and Criteria for Success, students engage with 1.OA.3, apply properties of operations as strategies to add and subtract, and 1.OA.4, understand subtraction as an unknown-addend problem, as they explain how they found the parts of their total. Workshop Written Assessment, “Students find the number pairs to make a total by guessing and checking, counting up, counting back, or using known facts. Exemplar Student Response, “My total is 6. I found the parts by picking a card and then counting up to the total. So I picked a 4. Then I counted up until I got to 6 because that’s the whole. I got 2 so that’s the other part. Then I recorded by putting 6 here because it’s the whole. Then I put 4 and 2 here because they are the parts. I wrote the equation 4 + 2 because I’m combining the parts = 6 because they make the whole.”

• Unit 3, Practice Workbook B, Activity: X-Ray Vision, students engage with 1.OA.6, adding and subtracting within 20, demonstrating fluency for addition and subtraction within 10, as they calculate the missing addend using counters. Partners to 10, “Place 10 counters on the floor next to a container. Tell students to close their eyes. Put one of the items into the container. Tell students to open their eyes and identify how many counters were put inside it. Continue the game, eliciting all partners to 10.”

• Unit 4, Practice Workbook B, Activity: Ten and Tuck, students engage with 1.OA.6, add and subtract within 20, as they use their fingers to make 10. “Directions: Tell students to show 10 fingers. Instruct them to tuck three (students put down the pinky, ring finger, and middle finger on their right hands). Ask them how many fingers are up (7) and how many are tucked (3). Then, ask them to say the number sentence aloud, beginning with the larger part (7 + 3 = 10), beginning with the smaller part (3 + 7 = 10), and beginning with the whole (10 = 3 + 7 or 10 = 3 + 7).”

• Unit 5, Lesson 5, Workshop, Intro Packet, students engage with 1.OA.6, add and subtract within 20, demonstrating fluency for addition and subtraction within 10, as they add three numbers rolled with number cubes, using the strategy of grouping facts they know or can easily figure out. Problem 1, “$$5 + 3 + 5$$.”

The materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade-level. Examples include but are not limited to:

• Unit 3, Lesson 4, Exit Slip, students engage with 1.OA.6, add and subtract within 20, as they use number bonds to help them solve. “Find the difference between the number cubes. Represent by completing the number bond and equation.” Cubes show the numbers 9 and 6.

• Unit 4, Practice Workbook B, Math Sprint A, students engage with 1.OA.6, add and subtract within 20, demonstrating fluency for addition and subtraction within 10, as they practice addition and subtraction facts on a Math Sprint. Problem 23, “___ - 6 = 3”

• Unit 5, Lesson 21, Exit Slip, students engage with 1.OA.6, adding and subtracting within 20, demonstrating fluency for addition and subtraction within 10, as they find the missing subtrahend of a subtraction equation. “Fill in the blank to make the equations true. 10 - ___ = 8 - 2.”

• Unit 6, Lesson 17, Exit Ticket, students engage with 1.NBT.5, given a two-digit number, mentally find 10 more without having to count, as they independently add ten to a number. Problem 1, “$$32 + 10 =$$____.”

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Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Students are given multiple opportunities to engage in real-world applications, especially during Math Stories, which include both guided questioning and independent work time, and Exit Tickets to independently show their understanding.

Materials include multiple routine and non-routine applications of the mathematics throughout the grade level. Examples include:

• Unit 1, Guide to Implementing AF Math, Math Stories, September, students engage with 1.OA.2, represent and solve addition and subtraction problems within 20, in a non-routine problem. Sample Problem 3, “Carla is making fruit salad. She uses 8 apples and 2 more bananas than apples. How many pieces of fruit has she used altogether? ”

• Unit 2, Guide to Implementing AF Math, Math Stories, October, students engage with 1.OA.1, use addition and subtraction within 20 to solve routine word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions. Sample Problem 13, “There were 20 kids at the haunted house. Then, some ran out screaming. Now there are only 5 kids in the haunted house. How many kids ran out screaming?”

• Unit 3, Guide to Implementing AF Math, Math Stories, November/December, students engage with 1.G.1, identifying shapes, in a non-routine problem. Sample Problem 3, “Sammy grabs a handful of pattern block shapes. He gets 2 triangles, 1 trapezoid, 2 squares, and 1 hexagon. Ari grabs a handful too. He gets 3 rhombuses, a rectangle and 2 triangles. They each count to see how many 4-sided shapes they got. Who got more four-sided shapes? Ari or Sammy?”

• Unit 5, Guide to Implementing AF Math, Math Stories, February, students engage in a non-routine problem with 1.OA.1, solve addition and subtraction word problems within 20, as students calculate take apart problems with both addends unknown. Sample Problem 3, “Ms. Russo had 20 awards to pass out to her class. Her class has boys and girls. How many could she pass out to the girls? (after they represent: Find at least 4 different solutions) ($$0 + 20$$ is a solution).”

Materials provide opportunities for students to independently demonstrate routine and non-routine applications of the mathematics throughout the grade level. Examples include:

• Unit 4, Workbook E, students engage with 1.MD.4, interpreting data with up to three categories and answering questions, and 1.OA.2, solving addition problems of three whole numbers with a sum less than 20, as they calculate routine add-to problems with the results unknown of three addends in a non-routine problem. Problem 11, “The class has 18 students. On Friday, 9 students wore sneakers, 6 students wore sandals, and 3 students wore boots. Use squares with no gaps or overlaps to organize the data. Write a number sentence to tell how many students were asked about their shoes on Friday.”

• Unit 5, Lesson 23, Lesson 15 Task, students engage with 1.OA.7, understand the meaning of the equal sign and determine if equations involving addition are true or false, as they solve a routine word problem asking them to determine if the total of two groups are equal. Problem 1, “Ben has 9 ladybugs and 5 crickets in his jar. Jill has 8 ladybugs and 7 crickets in her jar. Dad thinks they have the same amount of insects in each jar. Is Dad correct? Show and tell how you know.”

• Unit 8, Lesson 8, Exit Ticket, students engage with 1.MD.2 to solve a routine word problem, by expressing the length of an object as a whole number of length units by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps. “How much longer is pencil B than pencil A? Use your inch tiles to help you. Pencil B is ___ inch tiles LONGER than pencil A.”

##### Indicator {{'2d' | indicatorName}}

The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout the program materials. Examples include:

Conceptual understanding

• Unit 6, Lesson 13, Exit Ticket, students engage with 1.NBT.6, subtract multiples of 10 in the range of 10-90 from multiples of 10 in the range 10-90, as they represent and solve two subtraction problems on an exit ticket. Problem 1, “Represent and solve. 50-30” Problem 2, “Represent and solve. 90-40” Assessment and Criteria for Success, “Students will find the difference of two multiples of ten. They may use any strategy that works. If counting back with fingers, they should be able to explain, ‘I started with 90 and then counted back 40 by counting back by tens 4 times because 40 is 4 tens.’”

• Unit 7, Practice Workbook D, students engage with 1.NBT.2, understand that the two digits of a two-digit number represent amounts of tens and ones, as they write the number represented by images of sticks and dots. Problem 5, “Which number is represented?” Four rods are shown with five dots.

• Unit 9, Lesson 9, Introduction, students engage with 1.NBT.4, add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of ten, as they use a strategy that makes sense to them (cubes, sticks and dots, count on by tens, expanded notation addition). Students pick two cards such as 47 and 50 and find the total. Students are to choose a strategy such as “count all by tens and ones.” The students might say, “We can count all of the tens by ten and the ones by one. Like this, 10, 20, 30, 40, 50, 60, 70, 80, 90, 91, 92, 93, 94, 95, 96, 97).” Students may also choose to count on by tens and ones. A student might explain, “I just know that we have 47 right there, so then I can just count on by tens like this 47 -- 57, 67, 77, 87, 97 (can use tens sticks with cubes or sticks to help count on).”

Procedural skills (K-8) and fluency (K-6)

• Unit 3, Lesson 2, Exit Slip, students engage with 1.OA.6, adding and subtracting within 20, as they use number bonds to build addition equations. Problem 1, “Find the total of the number cubes. Represent by completing the number bond and the equation.” Two cubes are shown with 5 and 6 on them. A number bond frame is provided and “___ + ___ = ___.”

• Unit 4, Practice Workbook B, Number Bond Roll, students engage with 1.OA.6, add and subtract within 20, demonstrating fluency for addition and subtraction within 10, as they review number bonds allowing students to build and maintain fluency with addition and subtraction facts within 10. “Match partners of equal ability. Each student rolls one die. Students use the numbers on their own die and their partner’s die as the parts of a number bond. They each write a number bond, addition sentence, and subtraction sentence on their personal white boards.”

• Unit 5, Lesson 13, Exit Slip, students engage with 1.OA.6, add and subtract within 20, as they solve addition and subtraction problems by creating a fact family. “Find the rest of the fact family. 13 - 6 = 7”

Application

• Unit 2, Guide to Implementing AF Math, Math Stories, October, students engage with 1.OA.1, adding and subtracting within 20 to solve word problems. Sample Problem 12, “Zamira read 18 books. Some were about bugs. 2 were about snakes. How many books about bugs did she read?”

• Unit 3, Lesson 13, Exit Ticket, students engage with 1.OA.1, use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, as they solve a story problem. Problem 2, “I made 3 yellow paper chains and 5 blue paper chains. How many paper chains did I make?”

• Unit 4, Guide to Implementing AF Math, Math Stories, January, students engage with 1.OA.1, adding and subtracting within 20 to solve word problems. Sample Problem 10, “Diego wrapped 24 presents. Jessica wrapped 9. How many fewer presents did Jessica wrap than Diego?”

• Unit 5, Guide to Implementing AF Math, Math Stories, February, students engage with 1.OA.1, adding and subtracting within 20 to solve word problems, as they solve compare problems with the smaller number unknown. Sample Problem 13, “Shayla has 12 fewer pencils than Matthew. Matthew has 19 pencils. How many pencils does Shayla have?”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include:

• Unit 3, Lesson 9, Exit Ticket, students engage with 1.OA.1, using addition and subtraction within 20 to solve word problems, and 1.OA.6, adding and subtracting within 20, as they solve take apart problems (application) with both addends unknown (conceptual understanding). Problem 2, “There were 7 animals on the farm. Some were sheep and some were pigs. How many could be sheep and how many could be pigs? Show one combination using a number bond and an equation.”

• Unit 3, Lesson 19, Exit Ticket, students engage with 1.OA.1, use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions and 1.OA.6, add and subtract within 20, as they solve a story problem (application), as they solve problems within 20 (procedural skill). Problem 5, “Sarah has 9 pennies. Michael has 6 pennies. How many more pennies does Sarah have than Michael? You can use your cubes to help you solve.” Assessment and Criteria for Success, Exemplar Response, “Sara has 3 more pennies than Michael. I know because I built 9 cubes and 6 cubes and put them next to each other. They both have 6 cubes but Sarah has 3 more pennies than Michael.”

• Unit 4, Lesson 5, Exit Ticket, students engage with 1.MD.4, organize, represent, and interpret data; and answer questions about the data points, as they interpret the data presented on a pictograph (conceptual understanding) and use it to solve compare/difference unknown word problems (application). Problem 1, “How many more rainy days than sunny days?” Students are provided with a weather pictograph showing sunny days, rainy days, and cloudy days.

• Unit 9, Lesson 5, Exit Ticket, students engage with 1.NBT.4, add within 100 including a two-digit number and a one-digit number, using concrete models or drawings; understand that it is sometimes necessary to compose a ten, as they add a two-digit number by compose a ten (procedural skill), and explain how they solved the problem (conceptual understanding). Problem 1, “Solve. Show your work. 57 + 6 = ________. “ Problem 2, “How did you solve? Why?”

#### Criterion 2.2: Math Practices

Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs).

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The Standards for Mathematical Practice are identified and incorporated within mathematics content throughout the grade level. The Mathematical Practices are listed in the Unit Overviews as well at the beginning of each lesson.

There is intentional development of MP1 to meet its full intent in connection to grade-level content. Examples include:

• Unit 3, Lesson 14, Narrative engages students in making sense of a real-world situation. “Acting out will be a part of the Introduction today to provide support for students who may struggle to visualize these types of problems on their own immediately. Creating a representation that depicts what is happening in the story can be challenging, so teachers should be ready to support students with questions like ‘What do you know? What do you need to find out?’” Introduction, Step 1, “There were some butterflies in my net. Five of the butterflies escaped. There are still 7 butterflies in my net. How many butterflies were in my net to start?”

• Unit 7, Lesson 3, Understand: Introduce the Problem, “Pose the Problem- I’m going to read you a problem. As I read, I want you to make a mind movie just like we do in Math Stories to visualize what is happening and what we need to figure out. Dad bakes two small peach pies. Both small peach pies are the same size. Dad cuts one peach pie in halves. Dad cuts one peach pie in fourths. Dad says Max can eat just one piece of peach pie. Max loves peach pie and want to each the largest piece of peach pie. Which piece of pie does Max pick to eat? Show all of your mathematical thinking.”

• Unit 8, Lesson 11, Narrative encourages teachers to promote perseverance. “If students see that their representation does not match the story, they know that they have made an error and they need to represent differently before they solve.”

There is intentional development of MP2 to meet its full intent in connection to grade-level content. Examples include:

• Unit 3, Lesson 5, Introduction provides prompts to guide teachers that help students make sense of information. “What do you notice about these two number bonds showing addition and subtraction? They are the same parts and the same whole.” Later, in the Exit Ticket, Problem 1, students demonstrate how they made sense of the content. “Write an addition equation and a subtraction equation that match the number bond.” (Number bond with 11, 4, 7)

• Unit 5, Lesson 9, Narrative, “Students engage in MP 2 today when they represent a subtraction situation symbolically with equations and explain what each quantity represents (with part/part/whole understanding).”

• Unit 8, Lesson 3, Narrative, “Students reason abstractly (MP 2) about the relative length of objects or characters in stories. They decontextualize the relative lengths by drawing a picture, creating a logical representation of the problem. Bob, Andy, and Joe are comparing their heights. Bob is taller than Andy. Bod is shorter than Joe. Who is the tallest?”

##### Indicator {{'2f' | indicatorName}}

Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP3 to meet its full intent in connection to grade-level content. Examples include:

• Unit 2, Lesson 9, Exit Ticket, Problem 2, “Fallon put together her puzzle like this. She says she made a square. Is she correct? How do you know?” An image of a rhombus made up of four triangles is shown.

• Unit 3, Lesson 5, Introduction, students represent addition and subtraction scenarios with number bonds. The teacher asks, “How are addition and subtraction related? What’s the same about them? What’s different? How does the number bond show both addition and subtraction?”

• Unit 3, Lesson 26, Introduction, students solve a story problem during the workshop introduction. “Ajacia saw 8 fewer red birds than brown birds in her yard. She saw 15 brown birds. How many red birds did she see?” The teacher looks for accurate representations and calls up students to explain their representations. The student might say, “I drew 15 circles for the 15 brown birds and put a box around it. Then I drew 8 x’s because I know that she saw 8 fewer red birds so she saw the same amount but 8 less. I put a box around that. I then put another box with a ? to represent that we need to figure out how many red birds that was.”

• Unit 7, Lesson 1, Workshop Worksheet, students construct a viable argument for partitioning shapes into halves. “Draw a line to split each of these shapes into halves. How do you know they are half and half?” Students are provided with pictures of nine shapes: two triangles, one hexagon, two circles, one rectangle, two squares, and one oval.

• Unit 8 Assessment, students analyze the mathematical reasoning of others as they determine whether a fictional student measured the height of a tree correctly. Item 11, “Bobby says the tree is 4 toothpicks tall. Do you agree or disagree? Why?”

• Unit 9, Lesson 4, Share/Discussion, guiding questions are provided for teachers to lead students to analyze the reasoning of other students as they share how they added a two-digit number and a one-digit number. “2-3 students share their work/strategies (count on, make ten). What is the same about these strategies? What is different? Which strategy is more efficient?”

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Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP4 to meet its full intent in connection to grade-level content. Examples include:

• Math Stories Guide, Promoting Reasoning through the Standards for Mathematical Practice, MP4, “Math Stories help elementary students develop the tools that will be essential to modeling with mathematics. In early elementary, students become familiar with how representations like equations, manipulatives, and drawings can represent real-life situations.” Within the K-4 Math Stories Representations and Solutions Agenda, students are given time to represent, retell, and solve the problem on their own.

• Unit 3, Lesson 27, Introduction Task, “Hank grows 19 bean plants in his garden. A goat eats 6 of the bean plants. Hank buys 5 more bean plants to grow in his garden. How many bean plants does Hank now have in his garden? Show all of your mathematical thinking.” Narrative, “Today’s lesson also supports the development of MP5 as students have a large bank of tools and strategies to choose from when modeling and solving today. Students can use concrete objects, pictures, tape diagrams (1:1 or numerical), number bonds (1:1 or numerical), and /or equations as strategies/tools to model the problem.”

• Unit 6, Lesson 4, Narrative, students decompose numbers 10-99 into tens and ones by using cubes, pictures, or knowledge of place value. “Students will look at a number, decompose into tens and ones, and represent using literal pictures, sticks and dots or an equation.”

• Unit 9, Lesson 8, Introduction Step 2, “Yesterday we used cubes to help us solve. But today we won’t all have cubes….Could we show this with a picture? How could we show regrouping with a picture?”

There is intentional development of MP5 to meet its full intent in connection to grade-level content. Examples include:

• Unit 1, Lesson 9, Narrative, “Students engage in MP5 when they choose an appropriate strategy to determine the number that comes right before/after a number or between two numbers. Students may access the number line or hundreds chart as useful classroom tools that are always available to them, but it is expected that most students will use strategy such as using the pattern to count from a benchmark number or to just know the next number and some students might use place value understanding. All of these strategies and tools are highlighted and discussed as they come up.”

• Unit 3, Lesson 7, Exit Slip Question 1, “Solve for the unknown. Write an addition equation that shows the parts and whole. (You may use the number line but do not have to.)” The problem includes a number bond with 8 as the whole, 5 as one part, and one part blank. The problem also includes a number line.

• Unit 9, Lesson 10, Narrative, “Students also develop MP 5 as they choose from a variety of tools and strategies to add two-digit numbers today. They may use cubes, pictures, fingers, or expanded notation models to help them solve. They can count all, count on in increments, or use known facts. Students explain why they chose the tools/ strategies they did both orally through CFUs (check for understanding) in the workshop and in writing on their workshop packets.”

At times, the materials are inconsistent. The Unit and Lesson Overview narratives describe explicit connections between the MPs and content, but lessons do not always align to the stated purpose.

The materials do not provide students with opportunities or guidance to identify and use relevant external mathematical tools and resources, such as digital content located on a website.

##### Indicator {{'2h' | indicatorName}}

Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP6 to meet its full intent in connection to grade-level content. Many problems present students with the opportunity to attend to precision within the mathematics and the reasoning of the answer. Examples include:

• Unit 3, Lesson 4, Exit Slip Question 1, students use precision to find the difference between two numbers and write an equation to match the problem. “Find the difference between the number cubes. Represent by completing the number bond and the equation.”

• Unit 5, Lesson 4, Skeleton VA, students use precision to prove the associative property. “Associative Property: what happens when we are combining amounts and we group the amounts differently. We get the same total! When I add, it doesn’t matter how I group the numbers--the total is the same.” Students are provided with pictures of three dice showing four, three, and two dots, and group the numbers in three different ways to demonstrate that they always have nine dots in all.

• Unit 6, Lesson 6, Criteria for Success, students use precision to show place value. ‘Students will roll two dice to determine the digits in the tens place and ones place. Then they will need to figure out how many by using their understanding of place value. They will also need to represent the quantity with literal pictures or sticks and dots, and expanded notation. Scholars should be able to explain their representation by saying, “This number is 62. I know because there is a 6 in the tens place which means there are 6 groups of ten, so I drew ten sticks. There is a 2 in the ones place which means there are 2 ones so I drew 2 dots to show the 2 ones. Then I wrote 60 + 2 to show the value of the tens and ones.”

The instructional materials attend to the specialized language of mathematics. The materials use precise and accurate mathematical terminology. Examples include:

• Unit 2, Lesson 10, Introduction, Step 3, “Describe the shape. Take a minute and look closely at the shape. What are some attributes we notice about this cone? (as students share, generalize to bullets below- ‘Oh, you noticed that it rolls, so you thought about it MOVES!’ Be sure to use appropriate language for attributes and prompt kids to do so as well: ‘That’s called a vertex; say it again but this time say “vertex” instead of point.’”

• Unit 7, Lesson 2, Introduction, during a game the teacher develops vocabulary. “Step 1 says Look at the shape. Step 2 says Break it in Quarters. How can I break this rectangle in quarters?’ Students might say, ‘You should draw a line down the middle so that it’s in two equal parts. Then draw another line down the middle so it’s four equal parts.’”

• Unit 8, Lesson 9, the Criteria for Success has an exemplar student response using accurate terminology. “The knife is 2 inch tiles longer than the fork. I know because I measured each with inch tiles, match the inch tiles one to one, and I could see that the knife needed 2 extra inch tiles to measure it, so it was 2 inch tiles longer.”

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Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.

There is intentional development of MP7 to meet its full intent in connection to grade-level content. Examples Include:

• Unit 1, Lesson 8, Narrative, “Students engage with MP 7 today as they observe patterns in how we say and write numbers and apply those patterns to extend the sequence. Teachers help students to see more patterns today by using the structure of the hundreds chart. As noted above, the arrangement of the numbers into rows of ten helps students to see more clearly the pattern in the tens place. Students may also begin to recognize the structure of place value.”

• Unit 5, Lesson 5, Assessment and Criteria for Success, “Student solves to find the totals 18 and 13. Student shows how he/she grouped the numbers for both problems and how they made ten for number 2.” (Problem posed: 7 + 6 + 5)

• Unit 7, Lesson 6, Workshop Worksheet, students use their understanding of the structure of a circle and fractions to tell time to the nearest half hour. Question 3, “Draw the missing hands on the clock. Half past 4.” Students are provided a picture of a clock with no hands.

There is intentional development of MP8 to meet its full intent in connection to grade-level content. Examples Include:

• Unit 2, Lesson 3, Narrative, “They also engage with MP 8 as they use repeated reasoning to determine the ‘rule’ their partner is using to sort the shapes.”

• Unit 6, Lesson 2, Introduce the math, “Yesterday we got to compose numbers by counting by tens and ones, and drawing pictures to show how many. Today we’re going to use what we know to do the same thing, but with even BIGGER numbers! What do we notice about how we write the digits of numbers and how that relates to the number of towers and extra cubes?”

Unit 9, Lesson 2, Exit Ticket, students use regular repeated reasoning to relate what they have learned about adding a two-digit number and a multiple of ten using sticks and dots, to adding them using the strategy of expanded notation. Problem 2, “Solve using expanded notation. 37 + 50 = ____.”

### Usability

The materials reviewed for Achievement First Mathematics Grade 1 do not meet expectations for Usability. The materials partially meet expectations for Criterion 1, Teacher Supports, partially meet expectations for Criterion 2, Assessment, and do not meet expectations for Criterion 3, Student Supports.

##### Gateway 3
Does Not Meet Expectations

#### Criterion 3.1: Teacher Supports

The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content.

The materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the materials, include standards correlation information that explains the role of the standards in the context of the overall series, and provide a comprehensive list of supplies needed to support instructional activities. The materials contain adult-level explanations and examples of the more complex grade-level concepts, but do not contain adult-level explanations and examples and concepts beyond the current grade so that teachers can improve their own knowledge of the subject. The materials provide explanations of the instructional approaches of the program but do not contain identification of the research-based strategies.

##### Indicator {{'3a' | indicatorName}}

Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. Teacher guidance is found throughout the materials in the Implementations Guides, Unit Overviews, and individual lessons.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• The Guide to Implementing AF Math provides a Program Overview for the teacher with information on the program components and scope and sequence. This includes descriptions of the types of lessons, Math Stories, Math Practice, and Cumulative Review.

• The Math Stories Guide (K-4) provides a framework for problem solving.

• Each Unit Overview includes a section called “Key Strategies” that describes strategies that will be utilized during the unit.

• The Teacher’s Guide supports whole group/partner discussion, ask/listen fors, common misconceptions and errors.

• In the narrative information for each lesson, there is information such as “What do students have to get better at today? Where will time be focused/funneled?”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Each lesson includes anticipated challenges, misconceptions, key points, sample dialogue, and exemplar student responses. Examples from Unit 6, Two-Digit Numbers, Lesson 9 include:

• “What is new and/or hard about the lesson? This is challenging for students for two main reasons. They may have difficulty building/representing the two quantities and make mistakes when counting by tens. Teachers should encourage precision both when building/drawing quantities and counting by tens.”

• “Exemplar Student Response: Students should be able to explain their work by saying, “I drew 5 sticks because there are 5 tens and 0 dots because there are 0 ones. Then I drew 3 sticks because there are 3 more tens and 0 dots because there are 0 ones. I’m finding the total so I counted all of the sticks. I know each stick is worth 10 so I counted by tens: 10, 20, 30, 40, 50, 60, 70, 80.”

• “Potential Misconception: Student makes representing errors. Student makes calculation errors.”

• “Mid-Workshop Interruption: If > \frac{2}{3} of students are successfully solving and using a range of strategies, ask students to discuss what they notice about the digits and how they change. Which digit changes when we combine tens? Why do you think that happens? (Why doesn’t the ones place change?) If < \frac{2}{3} of students are successful, call students back together to clear up the misconception through a misconception protocol. Continue to circulate and check for students to apply the learning. Make note of student success in applying in your Rapid Feedback tracker to inform the path for the Discussion.”

• “Share/Discussion: Direct students to the Discussion work space in their packets as needed. Use workshop data to determine the appropriate path: Facilitate a discussion around a major misconception, Show non-example and related example: Which is correct? Why doesn’t ___’s work? OR, 2-3 students share their work strategies, What is the same about these strategies? What is different? OR, ask students to apply their learning in a new way with an additional exercise. Possible Extension Problem: Solve 15 + 30.”

Each lesson includes both “What” and “How” Key Point sections that describe what students should know and be able to do and how they will do it. Examples from Unit 6, Two-Digit Numbers, Lesson 9 include:

• “What Key Points: Two digit numbers are made up of tens and ones. Tens are made up of tens and thus can be counted by tens. A multiple of ten is a group of tens with no extra ones.

• “How Key Points: We can represent two-digit numbers by building them with cubes and creating tens sticks. We can represent two-digit numbers by drawing literal pictures. We can represent two-digit numbers by showing the tens with sticks and the ones with dots. We can combine two multiples of tens by counting all by tens. We can combine two multiples of ten by counting on by tens.”

##### Indicator {{'3b' | indicatorName}}

Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for  containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject. There is very little reference or support for content in future courses.

Materials contain adult-level explanations and examples of the more complex grade/course-level concepts so that teachers can improve their own knowledge of the subject. Examples include:

• Unit Overviews provide thorough information about the content of the unit which often includes definitions of terminology, explanations of strategies, and the rationale about incorporating a process. Unit 5 Overview, Identify the Narrative, “Make 10 is a valuable strategy in the base-ten system because it allows students to work flexibly with numbers to solve more challenging problems by breaking them down into easier problems that they can solve fluently. The building blocks for the make ten strategy are built in Kindergarten, as students become familiar with number partners for numbers 1-10, decompose teen numbers into a group of ten and some more ones.”

• The Unit Overview includes an Appendix titled “Teacher Background Knowledge” which includes a copy of the relevant pages from the Common Core Math Progression documents which includes on grade-level information.

Materials do not contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject. Examples include:

• The Common Core Math Progression documents in the Appendix are truncated to the current grade level and do not go beyond the current course.

##### Indicator {{'3c' | indicatorName}}

Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/series. Examples include:

• Guide to Implementing AF Grade 1, Program Overview, “Scope and Sequence Detail is designed to help teachers identify the standards on which each lesson within a unit is focused, whether on grade level or not. You will find the daily lesson aims within each unit and the content standards addressed within that lesson. A list of the focus MPs for each lesson and unit and details about how they connect to the content standards can be found in the Unit Overviews and daily lesson plans.”

• The Program Overview informs teachers “about how to ensure scholars have sufficient practice with all of the Common Core State Standards. Standards or parts thereof that are bolded are addressed within a lesson but with limited exposure. It is recommended that teachers supplement the lessons addressing these standards by using the AF Practice Workbooks to ensure mastery for all students. Recommendations for when to revisit these standards during Math Practice and Friday Cumulative Review are noted in the Practice section of each unit.”

• The Unit Overview includes a section called Identify Desired Results: Identify the Standards which lists the standards addressed within the unit and previously addressed standards that relate to the content of the unit.

• In the Unit Overview, the Identify The Narrative provides rationale about the unit connections to previous standards for each of the lessons. Future grade-level content is also identified.

• The Unit Overview provides a table listing Mathematical Practices connected to the lessons and identifies whether the MP is a major focus of the unit.

• At the beginning of each lesson, each standard is identified.

• In the lesson overview, prior knowledge is identified, so teachers know what standards are linked to prior work.

Explanations of the role of the specific grade-level/course-level mathematics are present in the context of the series. Examples include:

In the Unit Overview, the Identify the Narrative section provides the teacher with information to unpack the learning progressions and make connections between key concepts. Lesson Support includes information about connections to previous lessons and identifies the important concepts within those lessons. Examples include:

• Unit 8, Lesson 7, Narrative, “What do students have to get better at today? As a result of this lesson, students can order 3 objects that cannot be directly compared by applying what they have learned in the previous lessons about measuring with precision to measure each object, and comparing the measurements. What is new and/or hard about that? Students are familiar with ordering objects by length when they are able to compare them directly (lesson 1). They also are familiar with comparing numerals to see which is greater or less for Kindergarten (K.CC.7). Today, students combine the strategies they use to order objects (asking which is longest and shortest and in between).”

• In the Unit Overview, the standards that the unit will address are listed along with the previous grade level standards/previously taught and related standards. Also included is a section named “Enduring Understandings: What do you want students to know in 10 years about this topic? What does it look like in the unit for students to understand this?” For example, in Unit 8, standards addressed are 1.MD.1 and 1.MD.2. Previous Grade Level Standards/Previously Taught & Related Standards include 1.OA.1, 1.OA.2, K.MD.2, K.MD.1. An example grade level enduring understanding is, “The whole numbers are in a particular order that represents their magnitude. There are patterns in the way we say and write the numbers.” An example for what it looks like in this unit is, “Students apply the counting sequence when measuring by counting the number of units to determine length. Students also relate counting to addition when they use count up as a strategy for finding the difference in lengths.”

##### Indicator {{'3d' | indicatorName}}

Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for Achievement First Mathematics Grade 1 provides strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

• The Unit Overview includes a parent letter in both English and Spanish for each unit that includes information around what the students are working on and example strategies students will use. The letter includes information about common mistakes that parents can watch for as well as links to websites that can provide assistance.

• There is also a suggestion related to the Unit Overview, “This guide can be printed and sent home to families so that parents/guardians can better support their scholars with homework.”

##### Indicator {{'3e' | indicatorName}}

Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Materials explain the instructional approaches of the program.

• The Implementation Guide states, "Our program aims to see the mathematical practices come to life through the shifts (focus, coherence, rigor) called for by the standards. For students to engage at equal intensities weekly with all 3 tenets, we structured our program into three main daily components Monday-Thursday: Math Lesson, Math Stories and Math Practice. Additionally, students engage in Math Cumulative Review each Friday in order for scholars to achieve the fluencies and procedural skills required."

• The Implementation Guide includes descriptions of “Math Lesson Types.” Descriptions are included for Game Introduction Lesson, Task Based Lesson, Math Stories, and Math Practice. Each description includes a purpose and a table that includes the lesson components, purpose, and timing.

Materials do not include and reference research-based strategies.

• The materials do not explicitly name any strategies as research-based strategies.

##### Indicator {{'3f' | indicatorName}}

Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

Each lesson includes a list of materials specific to the lesson. Examples include:

• Unit 4, Lesson 4, the Lesson Overview includes, “Materials: Graph packets (1 per student, double-sided), Data vocab poster, Intro bar graph, and Rapid Feedback tracker.”

• Unit 8, Lesson 5, the Lesson Overview includes, “Materials: 9cm strip of paper, worksheet packets, measurement VA, rapid feedback tracker.”

##### Indicator {{'3g' | indicatorName}}

This is not an assessed indicator in Mathematics.

##### Indicator {{'3h' | indicatorName}}

This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for Assessment. The materials identify the standards, but do not identify the practices assessed for the formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for following-up with students. The materials include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

##### Indicator {{'3i' | indicatorName}}

Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed. There are connections identified for standards, but not the mathematical practices.

Materials identify the standards assessed for the formal assessments. Examples include:

• Each Unit Overview provides a chart that identifies CCSS Math Content standards for each item on the Unit Assessment. Occasionally, an individual item on the assessment identifies the standard, but in general, student-facing assessments do not include the standards.

• Each lesson includes an Exit Ticket that aligns with the standard of the lesson.

Materials do not identify the practices assessed for the formal assessments.

##### Indicator {{'3j' | indicatorName}}

Assessment system provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The assessment system provides multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but does not provide suggestions for following-up with students. Examples include:

• Assessments include an informal Exit Ticket in each lesson and a formal Unit Assessment for every unit.

• There is guidance, or “look-fors,” for teachers about what the student should be able to do on the assessments.

• All Unit Assessments include an answer key with exemplar student responses.

• Some units include a section titled “Evaluating Student Learning Outcomes” which provides a detailed description of what the student is expected to do.

• There are no strategies or suggestions if students do not demonstrate understanding of the concept, and no next steps based on the results of the assessment.

##### Indicator {{'3k' | indicatorName}}

Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. There are a variety of question types including multiple choice, short answer, and constructed response. Mathematical practices are embedded within the problems.

Assessments include opportunities for students to demonstrate the full intent of grade-level standards across the series. Examples include:

• In the Unit 3 assessment, the full-intent of standard 1.OA.1 (use addition and subtraction within 20 to solve word problems) is met. Item 1, “Maya had 3 books. Sean had 5 books. How many books did they have in all?” There are 12 available items, varied addition and subtraction situations, and space is provided for students to use objects, drawings, and equations to solve.

• In the Unit 6 assessment, the full-intent of standard 1.NBT.2 (understand that the digits in a 2-digit number represents tens and ones) is met. Item 3, “Which is not the same as 50 + 2? (multiple choice item with answer choices: 5 ones, 2 tens; quick tens image of 5 tens and 2 ones; 5 tens, 2 ones; 52).”

• In the Unit 7 assessment, the full-intent of standard 1.G.3 (partition circles and rectangles into two and four equal shares) is met. Item 2, “Which circle is partitioned into fourths? (MC item with four possible choices to choose from).” Item 7, “Show all of the ways that you could shade in half of the rectangles.” Eight blank rectangles are provided.

Assessments include opportunities for students to demonstrate the full intent of grade-level practices across the series. Examples include:

• Unit 3 Assessment, Item 11, supports the full development of MP2: Reason abstractly and quantitatively. “Which equation could you use to represent the problem: My teacher gave me 6 star stickers, 5 hear stickers, and 2 smiley face stickers. How many stickers do I have all together? 3 + 2 + __ = 5; 5 + 3 + 1 __; 3 + 5 + 2 = __; __ + 3 + 5 = 2.”

• Unit 5 Assessment, Item 9, supports the full development of MP3: Construct viable arguments and critique the reasoning of others. “Students were writing number sentences to figure out how many balloons and how many hats there were. (image of 3 balloons and 6 hats) Monica wrote 3 + 6 = 9. Terry wrote 3 + 6 = 9. a) Who is correct” (Answer choices - Monica only; Terry only; Both Monica and Terry; Neither Monica nor Terry) b) Why?”

• Unit 6 Assessment, Item 3, supports the full development of MP7: Look for and make use of structure. Assessment Item 3, “Which is not the same as 50+2? (Answer choices-5 ones, 2 tens; image of 5 lines to represent tens and 2 dots to represent ones; 5 tens, 2 ones; 52).”

##### Indicator {{'3l' | indicatorName}}

Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Achievement First Mathematics Grade 1 do not provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. This is true for both formal unit assessments and informal exit tickets.

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for Achievement First Mathematics Grade 1 do not meet expectations for Student Supports. The materials do not provide strategies and supports for students in special populations or for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level/series mathematics. The materials provide some extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials do provide manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

##### Indicator {{'3m' | indicatorName}}

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for Achievement First Mathematics Kindergarten do not meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials do not provide specific strategies and supports for differentiating instruction to meet the needs of students in special populations.

##### Indicator {{'3n' | indicatorName}}

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for Achievement First Mathematics Grade 1 partially meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Some lessons include an Extension/Application Problem that allows teachers to extend the thinking of the lesson during discussion. However, extension problems are intended for all students as there is no identified differentiation for advanced students. Examples Include:

• Unit 1, Lesson 3, Narrative, “some students will begin to understand that ten can be thought of as a single unit worth ten, and they may use that understanding to determine the value of a set without counting (ie – I see 3 tens and 4 ones; that is 34), though this is considered extension for this unit.” Extension/Application Problem states, “Zahara was making ice cubes for her lemonade stand. Each ice cube tray holds 10 ice cubes. (then show an image of ice cube trays full and one partially full; attached) How many ice cubes does she have? How do you know?”

• Unit 4, Lesson 4, Extension/Application problem extends student understanding of graphs by including the analysis of two graphs. “Alex asks his family what their favorite breakfast food is and created a bar graph to show the results. Ciana asked her family what their favorite breakfast food is and made a picture graph to show the results. The graphs are below. Which child had more people answer their survey? How do you know?”

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for Achievement First Mathematics Grade 1 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning; however, there are no opportunities for students to monitor their learning.

The program uses a variety of formats and methods over time to deepen student understanding and ability to explain and apply mathematics ideas. These include: Exercise Based Lessons, Task Based Lessons, Math Stories, Math Practice, and Cumulative Review.

In the lesson introduction, the teacher states the aim and connects it to prior knowledge. In Pose the Problem, the students work with a partner to represent and solve the problem. Then the class discusses student work. The teacher highlights correct work and common misconceptions. Then students work on the Workshop problems, Independent Practice, and the Exit Ticket. Students have opportunities to share their thinking as they work with their partner and as the teacher prompts student responses during Pose the Problem and Workshop discussions. Math Stories provide opportunities for students to question, investigate, sense-make, and problem-solve using a variety of formats and methods.

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Achievement First Mathematics Grade 1 provide some opportunities for teachers to use a variety of grouping strategies. Grouping strategies within lessons are not consistently present or specific to the needs of particular students. There is no specific guidance to teachers on grouping students.

The majority of lessons are whole group and independent practice; however, the structure of some lessons include grouping strategies, such as working in a pair for games, turn-and-talk, and partner practice. Examples include:

• Unit 3, Lesson 2, Introduce the Math, “Turn and remind your partner how a number bond shows the part/part.whole relationship.”

• Unit 9, Lesson 2, Narrative, “Students explain via a turn and talk in the intro and throughout the workshop as the teacher circulates and asks students how they solved and why it works. Students relate different strategies to one another in a turn and talk after the initial strategy share and and also potentially after strategy shares in the MWI and Discussion portion of the lesson.”

##### Indicator {{'3q' | indicatorName}}

Materials provide strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials reviewed for Achievement First Mathematics Grade 1 do not meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Materials do not provide any resources for students who read, write, and/or speak in a language other than English to meet or exceed grade-level standards through regular and active participation in grade-level mathematics.

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Achievement First Mathematics Grade 1 provide a balance of images or information about people, representing various demographic and physical characteristics. Examples include:

• Lessons portray people from many ethnicities in a positive, respectful manner.

• There is no demographic bias seen in various problems.

• Names in the problems include multi-cultural references such as Mario, Tanya, Kemoni, Jiang, Paige, and Tomi.

• The materials are text based and do not contain images of people. Therefore, there are no visual depiction of demographics or physical characteristics.

• The materials avoid language that might be offensive to particular groups.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Achievement First Mathematics Grade 1 do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials do not provide suggestions or strategies to use the home language to support students in learning mathematics. There are no suggestions for teachers to facilitate daily learning that builds on a student’s multilingualism as an asset nor are students explicitly encouraged to develop home language literacy. Teacher materials do not provide guidance on how to garner information that will aid in learning, including the family’s preferred language of communication, schooling experiences in other languages, literacy abilities in other languages, and previous exposure to academic everyday English.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Achievement First Mathematics Grade 1 do not provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials do not make connections to linguistic and cultural diversity to facilitate learning. There is no teacher guidance on equity or how to engage culturally diverse students in the learning of mathematics.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Achievement First Mathematics Grade 1 provide supports for different reading levels to ensure accessibility for students.

Strategies used include: teacher reading the problem, visualizing, and creating “mind-movies.” Examples include:

• In Unit 6 Lesson 22, Introduction, Pose the Problem, “I’m going to read you a problem. As I read, I want you to make a mind movie just like we do in Math Stories to visualize what is happening and what we need to figure out. Kevin is reading a book that has 50 pages. The second day, Kevin reads ten pages. The third day, Kevin reads ten pages. Kevin thinks he has 20 more pages to read. Is Kevin correct? Show and tell how you know.”

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for Achievement First Mathematics Grade 1 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Manipulatives are accurate representations of mathematical objects and are connected to written methods. Examples include:

• Unit 1, Lesson 2, to address standard 1.NBT.1(count to 120), the materials include bags of loose objects and a sorting mat. In Overview, Identify the Narrative, “Lesson 1 focuses on reviewing the kindergarten strategies of keeping track of the count, and then students quickly move into strategically grouping objects into sets of tens and extra ones in lesson 2.” Introduce the Math, “Yesterday we counted large groups of objects to figure out how many we had. Today, we are going to play Counting Jar again and look for even more efficient ways to figure out how many when we have a lot of something. Model the game but not the strategies. Step 1 says Take one bag. Step 2 says how many? How could we figure out how many?” Students share review strategies from the previous day: move and count and organize and count (line up/arrange in an array). The materials state, “We need a strategy to keep track. We can move them as we count them or we can line them up as we count them.”

• Unit 3, Lesson 1, to address standard 1.OA.5 (relate counting to addition and subtraction), the materials include bags of cubes with two colors. In the Overview, Identify the Narrative, “For all of these story problem types, students should be able to represent with cubes or another manipulative, a 1:1 picture, a 1:1 tape diagram and/or number bond, a numerical tape diagram and/or number bond, and an equation. Further, the student should be able to relate all of these representations to each other, articulating how they all represent the story.” Introduce the Math, “Students should have bags on carpet that match the teachers’ bags 1 and 2. Step 1: Pick a bag (Pick bag 1). Step 2: Represent parts and wholes.”

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for Achievement First Mathematics Grade 1 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, or provide teacher guidance for the use of embedded technology to support and enhance student learning. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for Achievement First Mathematics Grade 1 do not integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials do not contain digital technology or interactive tools such as data collection tools, simulations, virtual manipulatives, and/or modeling tools. There is no technology utilized in this program.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for Achievement First Mathematics Grade 1 do not include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials do not provide any online or digital opportunities for students to collaborate with the teacher and/or with other students. There is no technology utilized in this program.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for Achievement First Mathematics Grade 1 have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The student-facing printable materials follow a consistent format. The lesson materials are printed in black and white without any distracting visuals or an overabundance of graphic features. In fact, images, graphics, and models are limited within the materials, but they do support student learning when present. The materials are primarily text with white space for students to answer by hand to demonstrate their learning. Student materials are clearly labeled and provide consistent numbering for problem sets. There are several spelling and/or grammatical errors within the materials.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Achievement First Mathematics Grade 1 do not provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

There is no technology utilized in this program.

## Report Overview

### Summary of Alignment & Usability for Achievement First Mathematics | Math

#### Math K-2

The materials reviewed for Achievement First Mathematics Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades K-2 do not meet expectations for Usability, Gateway 3.

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

#### Math 3-5

The materials reviewed for Achievement First Mathematics Grades 3-5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades 3-5 do not meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

#### Math 6-8

The materials reviewed for Achievement First Mathematics Grades 6-8 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. The materials reviewed for Achievement First Mathematics Grades 6-8 do not meet expectations for Usability, Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations
###### Alignment
Meets Expectations
###### Usability
Does Not Meet Expectations

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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