K-2nd Grade - Gateway 1
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Focus and Coherence
Gateway 1 - Meets Expectations | 100% |
|---|---|
Criterion 1.1: Focus | 12 / 12 |
Criterion 1.2: Coherence | 8 / 8 |
The materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 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.
Criterion 1.1: Focus
Information on Multilingual Learner (MLL) Supports in This Criterion
For some indicators in this criterion, we also display evidence and scores for pair MLL indicators.
While MLL indicators are scored, these scores are reported separately from core content scores. MLL scores do not currently impact core content scores at any level—whether indicator, criterion, gateway, or series.
To view all MLL evidence and scores for this grade band or grade level, select the "Multilingual Learner Supports" view from the left navigation panel.
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 Amplify Desmos Math Kindergarten through Grade 2 meet expectations for focus. They assess grade-level content, clearly identify the content standards and mathematical practices assessed in formal assessments, offer opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series, and provide all students with extensive work on grade-level problems to support mastery of grade-level expectations.
Indicator 1a
Materials assess the grade-level content and, if applicable, content from earlier grades.
The materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.
The assessments are aligned to grade-level standards and do not include content from future grades. In Kindergarten through Grade 2, units include Mid Unit Check Ins, End of Unit Tests, and Performance Tasks. In Kindergarten, Sub-Unit Checklists and End-of-Unit Interviews may be used in place of Sub-Unit Quizzes and End-of-Unit Assessments. In Grades 1 and 2, Sub-Unit Quizzes and End-of-Unit Assessments are available in both print and digital formats. Starting in Grade 2, End-of-Unit Assessments are available in Forms A and B.
Examples include:
Kindergarten, Unit 4: Understanding Addition and Subtraction, End-of-Unit Assessment, Problem 3, students represent and solve a story problem. Problem 3 states, “There were 6 kids playing in the park. 2 of the kids left the park to go home. How many kids are playing in the park now? Show your thinking. There are ___ kids.” (K.OA.2)
Grade 1, Unit 2: Addition and Subtraction Story Problems, End-of-Unit Assessment, Problem 8, students determine if equations represent a story problem. Problem 8 states, “Circle 2 equations that can be used to solve this problem. Diego has 7 cubes. 4 of the cubes are black. The rest of the cubes are green. How many cubes are green? 4+3=74+3=7, 7−4=37−4=3,7+4=117+4=11.” (1.OA.4)
Grade 2, Unit 7: Adding and Subtracting Within 1000, Sub-Unit 1 Quiz, students add within 1,000 without composing. The Quiz states, "For Problems 2 and 3, find the sum. Show or explain your thinking. Problem 2. 613+245613+245. Problem 3. 368+414368+414." (2.NBT.7)
Indicator 1b
Assessment information is included in the materials to indicate which standards are assessed.
The materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 meet expectations for having assessment information included in the materials to indicate which standards are assessed.
Formal assessments, including Sub-Unit Quizzes and End-of-Unit Assessments, are consistently aligned to grade-level content standards and Mathematical Practice Standards. This alignment is clearly identified in the program’s Assess and Respond section.
Examples include:
Kindergarten, Unit 5 : Make and Break Apart Numbers Within 10, Sub-Unit 2 Quiz, Problem 2 states, "There are 7 students eating lunch at the table. Some of them are drinking milk. The rest are drinking water. How many students are drinking milk? How many students are drinking water? Show your thinking." The Assess and Respond Item Analysis denotes the standards assessed as K.OA.1, K.OA.2, and MP2.
Grade 1, Unit 3: Adding and Subtracting within 20, Sub-Unit 3 Quiz, Problem 4 states, “For Problems 4 and 5, solve the problem and write an equation to show how you solved it. Use an underline to show the answer in the equation. There are 5 red flowers, 7 purple flowers, and 3 white flowers in a vase. How many flowers are in the vase?” The Assess and Respond Item Analysis denotes the standards assessed as 1.OA.2, 1.OA.6, and MP2.
Grade 2, Unit 6: Geometry and Time, End-of-Unit Assessment: Form A, Problem 5 states, "Jada gets up in the morning at 6:45. Draw hands on the clock to show the time Jada wakes up. Then circle a.m. or p.m." An analog clock is provided. The Assess and Respond Item Analysis denotes the standards assessed as 2.MD.7 and MP6.
Indicator 1c
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 Amplify Desmos Math Kindergarten through Grade 2 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.
Summative assessments include Sub-Unit Quizzes and End-of-Unit Assessments. Each unit provides Assess and Respond guidance for both assessment types. In Kindergarten and Grade 1, the materials also include observation checklists to support teacher monitoring during assessments. Each lesson ends with Show What You Know tasks, which are optional in Kindergarten and Grade 1 and required in Grade 2. Assessments address grade-level content and practice standards using multiple item types, including multiple choice, multiple response, short answer, and extended response.
Examples include:
Kindergarten, Unit 5: Make and Break Apart Numbers Within 10 K.5 Sub-Unit 2 Checklist, Row c states, “After students complete/Revisit Choral Count Warm-Up in Lesson 10, say: ‘ Start at 17 and count forward by 1.’ (Stop the student around 50). Say, ‘How did you know what number to say after 17?’” Unit 6: Numbers 0–20, End-of-Unit Assessment, Problem 7 states, “Write the missing numbers. ___ 14 15 16 17 ___”. The materials assess the full intent of K.CC.2 as students count forward from a given number within the known sequence.
Grade 1, Unit 1: Adding, Subtracting, and Working With Data, 1.1 Sub-Unit 2 Quiz, Problem 5 states, “Circle to show if the equation is true or false. 6+1=2+66+1=2+6 Show or explain your thinking.” Students justify their conclusion with evidence or reasoning. Unit 7: Geometry and Time, 1.7 Sub-Unit 1 Checklist, Row a states, “Centers: Solid Shapes, Stage 3; Can You Draw It?, Stage 2, Make statements about the shapes students choose and have them respond with whether the statement is always, sometimes, or never true (e.g., Triangles have a corner at the top.).” Students analyze attributes of two- and three-dimensional shapes and determine whether each attribute is always, sometimes, or never true. Unit 7: Geometry and Time, End-of-Unit Assessment, Problem 6 states, “Diego says that the same amount of each square is shaded because 1 part of each square is shaded. Do you agree with Diego? Why or why not?” The materials assess the full intent of MP3 as students construct arguments to justify whether mathematical statements are true and critique the reasoning of others by agreeing or disagreeing with given claims using evidence.
Grade 2, Unit 1: Working with Data and Solving Comparison Problems, End-of Unit Assessment, Form A, Problem 8 states, “How many fewer students in the class were born in Connecticut than in New York? Show or explain your thinking.” Unit 2: Adding and Subtracting Within 100, End-of-Unit Assessment, Form A, Problem 7 states, “There were 19 rabbits at the animal rescue. There were 26 more dogs than rabbits at the rescue. How many rabbits and dogs were there altogether?” Unit 4: Addition and Subtraction on the Number Line, End-of-Unit Assessment, Form A, Problem 2 states, “Represent and solve the story problem. You may represent the problem with an open number line if it is helpful. Write an equation to represent the story problem and underline the answer in the equation. Marcos had a spool of yarn. Then Marcos added 20 more meters of yarn to the spool. Now the spool has 75 meters of yarn. How many meters of yarn did Marcos start with?” Unit 6: Geometry and Time, 2.6 Sub-Unit Quiz 1, Problem 2 states, “There are 17 shape cards in the pile. Some of them are triangles, and the rest are pentagons. How many of each shape could there be? Show your thinking.” The materials assess the full intent of 2.OA.1 as students solve one- and two-step addition and subtraction word problems within 100, including comparison and put-together/take-apart situations, with unknowns in different positions, and represent their thinking using equations or number lines.
Indicator 1d
Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials provide students with consistent opportunities to engage in the full intent of Grade K–2 standards. Each lesson includes a Warm-Up, one or more Activities, Lesson Practice, a Lesson Synthesis, and a Show What You Know task. Units also include Pre-Unit Checks to identify students’ prior knowledge and readiness for the unit content.
Examples include:
Kindergarten, Unit 2: Number 1–10, Lessons 5 and 11, and Unit 7: Solid Shapes All Around Us, Lesson 11 engages students with the full intent of 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, e.g., by using matching and counting strategies). Students use what they know about numbers to determine if quantities are more or less than a number. In Unit 2, Lesson 5, Activity 1, students apply their understanding of comparing quantities as they use their fingers to show more or fewer than a given quantity. Working in groups, students choose a card and flip it over, and then their partners hold up more or fewer fingers than are shown on the cards. Each partner tells how many fingers they are holding up, and both partners justify that the quantity represents their given comparisons. In Lesson 11, Activity 2, Problem 1, students draw groups of images that have more than, fewer than, or the same number of images as a group drawn by their partner. The Teacher Moves guides the teacher on how to play by inviting a student to act as a partner. The teacher says, “First, I will choose how many people are in a reservation and draw the group.” The teacher draws 7 images. The teacher says, “Then I will tell my partner if more, fewer, or the same number of people arrived at the restaurant. Fewer people arrived at the restaurant. My partner will draw a group that matches my sentence, tell how many are in the group, and compare the two groups using more, fewer, or the same number. Have the student partner draw a group that shows fewer, tell how many, and compare the groups.” In Unit 7, Lesson 11, Activity 1, Problem 1, students are directed to figure out and write a number to show how many of each shape they used and to tell their partner about the shapes using the words more, fewer, and same. The problem states, “Show Your Thinking” A blue triangle and an orange square are provided.
Grade 1, Unit 1: Adding, Subtracting, and Working With Data, Lessons 2–4 engage students with the full intent of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another). Students use data to interpret graphs. In Lesson 2, Activity 1, students create and share a data representation that shows how many shape cards are in each category to consider clear ways to share information. Problem 1 states, “Sort the shapes that Ying saw at the lake into 3 categories.” In Lesson 3, Activity 2, students share ideas for organizing and representing data to further develop their understanding of interpreting data. Problem 2 states, “Organize the cubes to help you count how many in each category.” In Lesson 4, Activity 2, students analyze and discuss data representations made by their peers to notice the parts of the representations that help them understand the data. Problem 2 states, “Discuss. Look at the data representation. Describe what you see, and explain how it helps you understand the data. I see _______. This helps me understand the data because ______.”
Grade 2, Unit 3: Measuring Length, Lessons 1, 5, and 9 engage students with the full intent of 2.MD.2 (Measure the length of an object twice, using length units of different lengths for the two measurements; describe how the two measurements relate to the size of the unit chosen). Students measure items using more than one unit. In Lesson 1, Warm-Up, students apply their understanding of non-standard measurements of length to describe the side lengths of a rectangle. Investigate: Orson’s Costumes states, “How could you help someone draw a rectangle they cannot see?” A sample response states, “The long sides are 4 big paper clips long. The short sides are 2 big paper clips and 2 little paper clips long.” In Lesson 5, Activity 2, Problems 4–6, students measure the lengths of objects using a meter stick to understand a new length unit and discuss why measuring long objects in longer length units is more efficient. The directions state, “You will measure strips of tape on the floor. Each tape strip represents the height of 1 of Orson’s trees. Measure the length of each tape strip in a combination of meters and centimeters. 4. What is the height of the teak tree? 5. What is the height of the rubber tree? 6. What is the height of the Kapok tree?” In Synthesis, the teacher displays a meter stick and a centimeter ruler. The Teacher Moves guidance states that the teacher should ask, “Would you choose to measure the classroom in centimeters or meters? Why? Would you choose to measure a book in centimeters or meters? Why?” In Lesson 9, Activity 2, students estimate and measure the lengths of objects, choosing the tools and units to use, to continue to develop their conceptual understanding of inches and feet. The problem states, “Pairs: Let’s estimate and measure the lengths of different objects. You’ll need: measuring tools (ruler, meter stick, tape measure), objects to measure, Recording Sheet. How to Play: 1. Choose an object to measure. 2. Partner A: Choose a unit to measure the length of the object you chose — inches, feet, centimeters, or meters. 3. Partner A: Estimate the length of your object and record your estimate. 4. Partner B: Choose a measurement tool — ruler, meter stick, or tape measure. 5. Partner B: Measure and record the actual measurement. 6. Switch roles and repeat until the Recording Sheet is full.” In Show What You Know, students are prompted, “Measure the length of an object in your classroom that is longer than 12 inches. Record the name of the object. Measure its length in inches using an inch ruler. Then measure its length in feet.”
The materials provide opportunities for students to meet the full intent of all Kindergarten through Grade 2 standards; however, they do not provide extensive work for all standards, with a missed opportunity for extensive work with one standard at Grade K and one standard at Grade 2.
Examples include:
Kindergarten, Unit 7: Solid Shapes All Around Us, Lesson 2, does not engage students in extensive work with K.G.3 (Identify shapes as two-dimensional (lying in a plane, “flat”) or three-dimensional (“solid”)). This is the only lesson that addresses K.G.3. In the Warm-Up, the teacher displays solid and flat shapes, and students share what they notice and wonder about the displayed shapes. In the Teacher Edition, at the end of the Warm-Up, the teacher closes by introducing flat and solid shapes, stating, “The shapes on top are called flat shapes. The shapes on the bottom are called solid shapes.” This is the only portion of the lesson that addresses flat and solid shapes. The remainder of the lesson focuses exclusively on solid shapes.
Grade 2, Unit 5: Numbers to 1,000, Lesson 3, does not engage students in extensive work with 2.NBT.1.b (Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones. Understand the following as special cases: The numbers 100, 200, 300, 400, 500, 600, 700, 800, 900 refer to one, two, three, four, five, six, seven, eight, or nine hundreds—and 0 tens and 0 ones). This is the only lesson that addresses 2.NBT.1.b. In this lesson, students build multiples of hundreds using hundreds and/or tens. In Activity 2, a Hands-On Problem states, “Draw base-ten diagrams, using only hundreds and tens, to represent 700 in 3 or more different ways.” Students could respond by drawing combinations of hundreds and tens, rather than building the number using only hundreds. In the Teacher Moves, during the Synthesis, the teacher prompts, “As you watch the animation, think about how you could compose 1,000 with hundreds, tens, or ones.” The teacher then asks, “How many hundreds would you need to compose 1,000? Tens? Ones? How do you know?” and closes with, “There are many ways to compose numbers with hundreds, tens, and ones. Noticing the relationship between the units can help you figure out how many hundreds, tens, and ones you can use.” Based on this single lesson, students are not provided the opportunity to develop the understanding that multiples of hundreds are composed of a certain number of hundreds, zero tens, and zero ones.
Indicator 1d.MLL
Materials assess the grade-level content and, if applicable, content from earlier grades.
The instructional materials reviewed for Grades K-2 of Amplify Desmos Math meet the expectations of providing support for MLLs’ full and complete participation in extensive work with grade-level problems to meet the full intent of grade-level standards.
The materials provide consistent, embedded strategies and scaffolds that enable MLLs to access and engage with rigorous, grade-level mathematical content. The materials intentionally designed these supports to develop both language and content knowledge through structured routines and opportunities for discourse across all four language domains—listening, speaking, reading, and writing. The Overview of each grade level outlines Amplify Desmos Math as a “structured approach to problem-based instruction,” in which lessons begin with a Warm-Up, then engage students with one to three instructional Activities, and end with a Synthesis. Each aspect of this instructional design is supportive of MLLs’ full and complete participation in extensive work with grade-level problems in various ways.
Warm-Ups activate prior knowledge of lived experiences or mathematics content from previous lessons, units, or grade levels. Warm-Ups may also provide a preview of a calculation that will appear in the Activities for the lesson. Because of this inclusion, Warm-Ups provide MLLs with a preview into the language they will use within the lesson, supporting them with full and complete participation.
Activities provide students with an opportunity to work in partners or small groups to “notice, wonder, explore, calculate, predict, measure, explain their thinking, settle disputes, create challenges for their classmates, and more.” This provides MLLs with ample opportunities to use and develop disciplinary language daily. Additionally, activities feature multimodal instruction, which creates accessible entry points for MLLs and structured opportunities for disciplinary language usage alongside mathematics learning. Real-life and animated videos provide MLLs with visual supports to engage fully in the mathematics and discourse of the lesson. Each lesson includes digital interactions designed to “pique students’ interest and invite all students to engage in mathematics.” Students’ digital experience involves engaging with mathematical concepts through dynamic digital interactives with responsive, immediate feedback and social, collaborative features such as the Share With Class button in which students can exchange ideas with others directly on an Activity screen. Additionally, the teacher can anonymize student submissions to “help them feel more comfortable sharing their ideas.” These digital features allow teachers to easily monitor as partners or small groups work and facilitate whole-class discussions to connect students’ ideas and synthesize the key concepts from the Activity.
Syntheses typically feature an open-ended prompt that invites students to “put key ideas from the lesson into their own words.” This supports MLLs’ understanding of the key math concepts by encouraging everyday language usage. Syntheses conclude with a whole-class discussion designed to synthesize learning and metacognitively reflect about mathematics of the Activities. The end of the Synthesis also provides “an opportunity for students to revise their responses after the discussion,” providing MLLs with an opportunity to refine their initial everyday language usage from the open-ended prompt, if needed.
As described in the report for 3e.MLL, the Overview for each grade level also features a Math Language Development section that outlines the material’s four-pronged approach to embedded supports for math language development for MLLs: vocabulary development, Language Goals, Math Language Routines, and Multilingual/English Learners Support. For more detailed information on vocabulary development and Language Goals, see the reports for 2j.MLL and 1.2.MLL-2, respectively. In addition to vocabulary development and Language Goals, each lesson features at least one Math Language Routines and one Multilingual/English Learners Support.
Math Language Routines [MLRs]: The materials consistently employ adapted versions of the MLRs by Stanford University UL/SCALE, which designed the MLRs to support the simultaneous development of mathematical practices, content, and language. “These routines are used within lessons to do one or more of the following: highlight student-developed language and ideas, cultivate conversation, support mathematical sense-making, and promote meta-cognition.”
MLR1: Stronger and Clearer Each Time helps students develop their ideas and language in verbal or written responses.
MLR2: Collect and Display invites the teacher to gather the language students use so that they can refer to and build on them in future discussions, which “increases accessibility and makes connections between informal and formal mathematical language.”
MLR3: Critique, Correct, Clarify supports students with error analysis, and with “communicating conceptual errors and ambiguities in language.”
MLR4: Information Gap creates a need for students to communicate by “giving partners or team members different pieces of necessary information that must be used together to solve a problem.”
MLR5: Co-Craft Questions provides an opportunity for students to “practice producing the language used in mathematical question asking” and to make sense of a context without the pressure to produce answers.
MLR6: Three Reads is intended to support “making sense of language and reading comprehension” when reading a mathematical text.
MLR7: Compare and Connect aims to make sense of multiple solution strategies for the same problem, specifically through teacher prompts designed to “identify, compare, and contrast multiple strategies.”
MLR8: Discussion Supports provides various linguistic supports to “encourage precise and meaningful student discussion,” such as: pressing for details, sentence frames, making a conjecture, or revoicing.
Multilingual/English Learners Supports [ML/EL Supports]: “Supports for Multilingual/English Learners are called out at intentional points within each lesson. These suggested supports are specific, targeted actions that are beneficial for Multilingual/English Learners. They often describe a modification to increase access to the task or support with contextual or mathematical language development that can often be supportive of all learners. ML/EL Supports may also be attached to MLRs.”
In addition to these embedded lesson features, the materials also feature Instructional Routines, which “create opportunities for conversations and support meaningful discussion,” as stated in the Instructional Routines section of each grades’ Overview. Like the MLRs, Instructional Routines are supportive of MLLs’ full and complete participation in extensive work with grade-level problems when they are used repeatedly. They “create efficiencies for teachers so that they can attend to student thinking and communicate what is important in their classroom. Instead of focusing on the directions of an activity, students can focus on making sense of and communicating about the math.” The materials implement the following Instructional Routines: Decide and Defend, Notice and Wonder, Number Talk, Tell a Story, Think-Pair-Share, Which One Doesn’t Belong?, Choral Count, Estimation Exploration, Gallery Tour, How Many Do You See? Mix and Mingle, Stories and Questions, True or False?, and What Do You Know About ____? More information on the Instructional Routines and MLRs, including implementation guidance, can be found in the Instructional Routines section of the digital PD Library.
To support MLLs’ full and complete participation, each lesson features a Math Language Development [MLD] Resource for one Activity. The MLD Resources Overview in each grade’s Overview states that this resource "provides additional support for integrating math language acquisition and development into each lesson.” The linguistic supports in this supplemental resource target moments of listening, speaking, reading, and/or writing in one Activity. The MLD Resources feature one Teacher Guide page and one or more Student Pages. The Teacher Guide includes a summary of the language demands of the Activity, categorized by collaborative language, interpretive language, and productive language. This provides teachers with information they need to anticipate the language demands of the Activity. The Teacher Guide then lists Spanish cognates and includes a section with teacher prompts to guide small-group or one-on-one discussions aligned with the Activity the MLD Resources support. These teacher prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging. The leveled supports suggested in the teacher guidance follow a predictable pattern across lessons and grades; the MLD Resources Overview describes the leveled supports on a general level:
“Emerging: Look for students to respond with gestures or single words as they begin to understand and use mathematical and contextual vocabulary.
Expanding: Look for students to respond using phrases or simple, complete sentences as they develop their English language skills and learn a greater variety of vocabulary and language structures.
Bridging: Look for students to respond in longer, complete sentences as they continue developing and applying their English language skills across various contexts.”
The Student Pages are aligned to the Activity and the Language Goals of the lesson, and they frequently contain sentence frames and starters, graphic organizers, and/or bilingual English-Spanish word banks. This does not add significant time to the overall lesson, and it supports MLLs’ full and complete participation in the single Activity that the MLD Resources supports in each lesson. While supportive, the MLD Resources present logistical barriers that may reduce the accessibility and consistent application of MLL supports. As a supplemental resource, these supports appear in a separate PDF on the digital platform, and in a separate print Resource Book, requiring teachers to navigate outside of the main lesson flow to locate them.
The materials offer teacher guidance to support them in fostering a positive mathematical community in their classrooms. The Math Identity and Community section of each grades’ Overview states, “The Math Identity and Community feature supports teachers in helping students build confidence in their own mathematical thinking, develop skills to work with and learn from others when doing math, and learn how math is an interwoven part of their broader community.
Each classroom is a unique combination of students, teachers, and school cultures… Teachers can use the suggested prompts to broaden students’ ideas about what it means to be good at math, highlight the value of each student’s contributions, and celebrate math class as a place for coming together to think in flexible, creative, and interesting ways. These habits of mind can help students engage with math joyfully and successfully both in and outside of math class.” This feature offers guidance aligned with the program's stated goal of supporting all students, including MLLs, in participating in the classroom community.
Criterion 1.2: Coherence
Each grade’s materials are coherent and consistent with the Standards.
The materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 meet expectations for coherence. They address the major work of the grade, connect supporting content to the major work, and make meaningful connections across clusters and domains. The materials also clearly highlight how grade-level content builds on knowledge from prior grades and lays the foundation for future learning.
Indicator 1e
When implemented as designed, the majority of the materials focus on the major clusters of each grade.
The materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 75 percent of instructional time to the major clusters of the grade:
In Grade K:
The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 5 out of 7 which is approximately 71%.
The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 90 out of 118, which is approximately 76%.
The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 109 out of 137, which is approximately 80%.
In Grade 1:
The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 5 out of 7 which is approximately 71%.
The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 92 out of 123, which is approximately 75%.
The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 122 out of 154, which is approximately 79%.
In Grade 2:
The approximate number of units devoted to major work of the grade (including supporting work connected to the major work) is 6 out of 8 which is approximately 75%.
The approximate number of lessons devoted to major work (including supporting work connected to the major work) is 95 out of 125, which is approximately 76%.
The approximate number of days devoted to major work of the grade (including supporting work connected to the major work) is 125 out of 155, which is approximately 81%.
An instructional day analysis across Grade K through Grade 2 is most representative of the instructional materials as the days include major work, supporting work connected to major work, and the assessments embedded within each unit. Any day marked optional was excluded. As a result, approximately 80% of the materials in Grade K, 79% of the materials in Grade 1, and 81% of the materials in Grade 2 focus on major work of the grade.
Indicator 1f
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
Materials are designed so that supporting standards/clusters are connected to the major standards/ clusters of the grade. These connections are listed for teachers within the Teacher Edition.
Examples include:
Kindergarten, Unit 7: Solid Shapes All Around Us, Lesson 11, Activity 1, connects the supporting work of K.MD.3 (Classify objects into given categories; count the numbers of objects in each category and sort the categories by count) to the major work of 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, e.g., by using matching and counting strategies). Activity 1, Directions state “Use blue rhombuses and orange squares to fill the birdhouse. Figure out and write a number to show how many of each shape you used. Tell your partner about your shapes using the words more, fewer, and same.” The Teacher Moves Launch states, “Say: ‘Use blue rhombuses and orange squares to fill the birdhouse. Figure out and write a number to show how many rhombuses and squares you used. Then compare the number of rhombuses you used and the number of squares you used. Tell your partner about the groups using the words more, fewer, and same and explain how you compared the 2 groups.’ Provide access to 10-frames.”
Grade 1, Unit 2: Addition and Subtraction Story Problems, Lesson 16, Activity 1, Problems 1–3, connect the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 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). Student Edition, Activity 1 states, “Look at the table of data about students’ favorite jobs in the garden. 1. Discuss what questions you could ask about two categories of data. 2. Write a question you want to answer about the data. 3. Find the answer to the question you wrote in Problem 2. Write an equation to show how you solved the problem. Use an underline to show the answer in the equation.”
Grade 2, Unit 1: Working with Data and Solving Comparison Problems, Lesson 11, Activity 2, connects the supporting work of 2.MD.10 (Draw a picture graph and a bar graph with single-unit scale) to the major work of 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem). Activity 2 states, “Use Benita’s bar graph to answer Problems 3 and 4. Write an equation that represents your thinking and underline the answer. Problem 3. How many total students voted for basketball or soccer? Problem 4. How many more students chose soccer than basketball?”
Indicator 1g
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 Amplify Desmos Math Kindergarten through Grade 2 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.
Connections among the major work of the grade are present throughout the materials where appropriate. These connections are listed for teachers in the Teacher Edition within each Unit Overview and may appear in one or more phases of a typical lesson: Warm-Up, Activity, Synthesis, Centers or Show What You Know.
Examples include:
Kindergarten, Unit 4: Understanding Addition and Subtraction, Lesson 3, Lesson Practice 4.03 connects the major work of K.CC.A (Know number names and the count sequence) to the major work of K.CC.B (Count to tell the number of objects). Problems 1-3 state, “Directions 1–3. Figure out the total number of trees. Write the total on the line.” Students are shown images of different trees and determine the total number by combining two organized groups, with a total of up to 10 images.
Grade 1, Unit 4: Numbers to 99, Lesson 10, Lesson Practice 4.10 connects the major work of 1.NBT.A (Extend the counting sequence) to the major work of 1.NBT.B (Understand place value).Problem 5 states, “Circle 3 representations that show 53.” Students are shown images of green base-ten blocks representing 3 tens and 5 ones, and orange blocks representing 5 tens and 3 ones. They are given multiple choice options to select an expression that matches the representations, such as 30+530+5, 50+350+3, 5 tens and 3 tens, or 5 tens and 3 ones.
Grade 2, Unit 7: Adding and Subtracting Within 1,000, Lesson 8, Lesson Practice 7.08 connects the major work of 2.NBT.A (Understand Place Value) to the major work of 2.NBT.B (Use place value understanding and properties of operations to add and subtract). Problem 2 states, “Clare’s drawing for finding the sum of 167+453167+453 is shown. Show Clare’s strategy using equations. Show your thinking.”
Indicator 1h
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 instructional materials reviewed for Amplify Desmos Math Kindergarten through Grade 2 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 Teacher Edition includes Unit and Lesson Overviews that identify content standard connections. Each Unit features a "Math of the Unit" section and a "Connections to Future Learning" component, both of which illustrate how current concepts relate to prior and future standards within the course and across grade levels. At the lesson level, materials specify the standards addressed and indicate how each lesson builds on prior learning, addresses current content, and/or prepares for future learning, categorized as Building On, Addressing, or Building Toward.
An example of a connection to future grades in Kindergarten includes:
Unit 2: Numbers 1–10, Connections to Future Learning connects 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, e.g., by using matching and counting strategies) to the work related to comparing quantities (1.NBT.3). Connections to Future Learning states, “In this unit, students use the terms more, fewer, less, and same when comparing quantities up to 10. In Grade 1, Unit 4, students will use <, >, and = symbols to compare quantities up to 100. Examples: Compare the numbers. Write <, >, or = to make each statement true. 95 > 59, 54 = 54. Write numbers to make each statement true. 65 > , < 84.”
An example of a connection to prior knowledge in Kindergarten includes:
Unit 5: Make and Break Apart Numbers Within 10, Lesson 2, Overview connects K.OA.3 (Decompose numbers less than or equal to 10 into pairs in more than one way, e.g., by using objects or drawings, and record each decomposition by a drawing or equation (e.g. 5=2+35=2+3 and 5=4+15=4+1 to the work related to counting and comparing numbers from 1 to 10. Prior Learning states, “In Unit 2, students counted and compared numbers from 1 to 10. In Unit 4, students developed an understanding of addition and subtraction as they represented and solved story problems and expressions.”
An example of a connection to future grades in Grade 1 includes:
Unit 6: Measuring Lengths of up to 120 Length Units, Connections to Future Learning connects 1.MD.2 (Express 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. Limit to contexts where the object being measured is spanned by a whole number of length units with no gaps or overlaps) to the work related to understanding place value (2.NBT.1and 2.NBT.2). Connections to Future Learning states, “In this unit, students count, read, write, and represent numbers to 120, within the context of length measurement. In Grade 2, Unit 5, students will extend this understanding to count within 1,000 and recognize that the 3 digits of a three-digit number represent amounts of hundreds, tens, and ones. Example: 983 is equal to 9 hundred, 8 tens, and 3 ones.”
An example of a connection to prior knowledge in Grade 1 includes:
Unit 3: Adding and Subtracting Within 20, Lesson 5, Overview connects 1.NBT.2a (10 can be thought of as a bundle of ten ones — called a “ten.” b) to the work related to composing teen numbers with 10 (K.NBT.1). Prior Learning states, “In Kindergarten, students recognized that teen numbers are composed of 10 ones and some more ones and described these numbers using language such as ‘10 and some more’ or ‘10 and 5 more.’”
An example of a connection to future grades in Grade 2 includes:
Unit 8: Equal Groups, Connections to Future Learning connects 2.OA.4 (Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends) to the work related to interpreting products using context (3.OA.1). Connections to Future Learning states, “In this unit, students arrange objects into equal rows and equal columns and find the total using addition. In Grade 3, Unit 1, students will relate repeated addition to multiplication and use their understanding of arrays to represent and solve multiplication problems. Example: The library invites guest readers each month. Their photos are arranged in 3 rows. Each row has 4 photos. Represent the situation with an array. Then write a multiplication expression to represent the display.”
An example of a connection to prior knowledge in Grade 2 includes:
Unit 2: Adding and Subtracting Within 100, Lesson 21, Overview connects 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem) to the work related to finding unknown addends for subtraction (1.OA.3). Prior Learning states, “In Lesson 20, students solved two-step problems with 2 or 3 given values and justified whether a story problem had more than 1 unknown. In Grade 1, students represented and solved Put Together/Take Apart, Total Unknown story problems to informally explore the Commutative Property of Addition.”