Alignment: Overall Summary

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten partially meet expectations for alignment to the CCSSM. The materials meet expectations for Gateway 1, focus and coherence. The instructional materials meet expectations for not assessing topics before the grade level in which the topic should be introduced, spend approximately 71% of instructional time on the major work of the grade, and are coherent and consistent with the standards. The instructional materials partially meet expectations for Gateway 2, rigor and the Mathematical Practices. The instructional materials meet expectations for rigor, attending to procedural skill and fluency and conceptual understanding, and they do not always treat the three aspects of rigor together or separately. The instructional materials identify and use the Mathematical Practices (MPs) to enrich grade-level content, but do not provide students with opportunities to meet the full intent of all MPs. The instructional materials meet expectations for students constructing viable arguments and analyzing the arguments of others and also for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others.

See Rating Scale Understanding Gateways

Alignment

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Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
15
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
N/A
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for Gateway 1, focus and coherence. The instructional materials meet the expectations for focus by assessing grade-level content and spend approximately 71% of instructional time on the major work of the grade. The instructional materials meet expectations for being coherent and consistent with the standards. 

 

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for assessing grade-level content. The instructional materials do not assess topics before the grade level in which they should be introduced.

Indicator 1a

The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.
2/2
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for assessing grade-level content. Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year.

Examples of aligned assessment items include but are not limited to:

  • Beginning-of-Year Assessment, Item 6, “Give children a bag with 20 connecting cubes. Say, ‘Show me 5 cubes.’ Note whether children count out 5 cubes and the strategies they use to keep track of their counting. You may wish to repeat with other numbers of cubes (up to 20) until the task becomes too challenging.” (K.CC.5)
  • Mid-Year Assessment, Item 1B, “Prompt children to count by 10’s. Stop them when they reach 100 or when their counting becomes erratic. Look for children to count by 10’s through 50.” (K.CC.1)
  • End-of-Year Assessment, Item 15, “Give children a bag with 15 craft sticks and tell them how many sticks it contains. First ask them to predict how many bundles of 10 and how many single sticks they will have if they bundle the sticks in groups of 10. Then have them bundle the sticks in this way and write a number sentence to describe their grouping. Look for children to predict that they can decompose 15 into a group of 10 ones and 5 more ones and then bundle the craft sticks to show this decomposition. Also, look for them to record this grouping with an equation: 15 = 10 + 5 or 10 + 5 = 15.” (K.NBT.1)

Criterion 1b

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
4/4
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Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for spending the majority of time on major work of the grade. The instructional materials, when used as designed, spend approximately 71% of instructional time on the major work of the grade, or supporting work connected to major work of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for spending a majority of instructional time on major work of the grade.

  • There are 9 instructional sections, of which 7 sections address major work of the grade or supporting work connected to major work of the grade, approximately 78%.
  • There are 117 lessons, of which 83 address major work of the grade or supporting work connected to the major work of the grade, approximately 71%.
  • In total, there are 170 days of instruction (125 days of lessons and 45 flex days), of which 86 days address major work of the grade or supporting work connected to the major work of the grade, approximately 51%. 
  • Within the 45 Flex days, the percentage of major work or supporting work connected to major work could not be calculated because the materials suggested list of differentiated activities do not include explicit instructions. Therefore, it cannot be determined if all students would be working on major work of the grade.

The number of lessons devoted to major work is most representative of the instructional materials. As a result, approximately 71% of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for being coherent and consistent with the standards. The instructional materials have supporting content that engages students in the major work of the grade and content designated for one grade level that is viable for one school year. The instructional materials are partially consistent with the progressions in the standards, and the materials foster coherence through connections at a single grade.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of supporting standards/clusters connected to the major standards/clusters of the grade include but are not limited to:

  • In Lesson 1-2, Focus: Exploring Pattern Blocks, students are introduced to 6 pattern blocks. The teacher asks, “How many sides does the square have? Name or point to another shape with four sides. Do all the shapes with fours sides look the same?” This connects supporting standard K.G.2, “Correctly name shapes regardless of their orientations or overall size,” to the major work of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”
  • In Lesson 2-7, Focus: Solving the Open Response Problem, students sort a collection of items according to attributes into different categories and then count the items. This connects the supporting work of K.MD.1, “Describe measurable attributes of objects, such as length and weight. Describe several measurable attributes of a single object,” to the major work of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”
  • In Lesson 3-1, Focus: Graphing Pattern Blocks, students sort pattern blocks into different categories and then compare the categories by answering questions involving fewer and greater. This connects the supporting work of K.MD.3, “Classify objects into given categories; count the numbers of objects in a category,” 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.”
  • In Lesson 4-1, Focus: Exploring Attribute Blocks, students classify and sort attribute blocks by their shape and size and count and compare the number of blocks in each group. This connects the supporting work of K.MD.3, “Classify objects into given categories; count the numbers of objects in a category” and K.G.2 “Correctly name shapes regardless of their orientations or overall size,” 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.”
  • In Lesson 9-4, Focus: Measuring and Comparing Backpacks, students compare the heights of two different backpacks using connecting cubes to measure. This connects the supporting work of K.MD.1, “Describe measurable attributes of objects, such as length and weight. Describe several measurable attributes of a single object,” to the major work of K.CC.7, “Compare two numbers between 1 and 10 presented as written numerals.”

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations that the amount of content designated for one grade level is viable for one year. 

Recommended pacing information is found on page xxii of the Teacher’s Lesson Guide and online in the Instructional Pacing Recommendations. The instructional materials include pacing for 170 days of instruction: 

  • There are 9 instructional sections with 117 lessons. Beginning in Section 2, Open Response/Reengagement lessons require 2 days of instruction adding 8 additional lesson days.
  • There are 45 Flex Days that can be used for lesson extension, extra game time, differentiation, or connection activities; however, explicit teacher instructions are not provided.
  • There are 3 embedded face-to-face assessments, Beginning-of-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment, spanning multiple days.   

The materials note that lessons are 45-60 minutes and consist of 3 components: Daily Routine: 10-15 minutes; Core Activity: Focus; 20-30 minutes; and Core Activity: Practice: 10-15 minutes.

Indicator 1e

Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
1/2
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten partially meet expectations for being consistent with the progressions in the Standards. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades, but there are some lessons that contain content from future grades that is not identified as such. There are also standards for which the materials do not present extensive work.

The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades. Each Section Organizer contains a Coherence section with “Links to the Past”. This section describes “how standards addressed in the Focus parts of the lessons link to the mathematics that children have done in the past.” Examples include:

  • Teacher’s Lesson Guide, Section 1 Organizer, Coherence, “Links to the Past” for K.CC.1, “In PreK, children learned and practiced the count sequence through 10 (and beyond as ready) through playful counting games, songs, and movement activities.”
  • Teacher’s Lesson Guide, Section 2 Organizer, Coherence, “Links to the Past” for K.OA.1, “In Pre-K, children represented addition and subtraction by acting out number stories either physically or concretely with manipulatives.”
  • Teacher’s Lesson Guide, Section 4 Organizer, Coherence, “Links to the Past” for K.MD.1, “Children described lengths of objects in Kindergarten lessons 1-1 and 3-5. In Pre-K, children used the terms big and small to describe measurable attributes and began to learn about different size dimensions, such as length and weight.”
  • Teacher’s Lesson Guide, Section 5 Organizer, Coherence, “Links to the Past” for K.NBT.1, “Children informally explored numbers 11 through 20 earlier in Kindergarten and in PreK, through various oral and rational counting activities.”
  • Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Past” for K.G.3, “In PreK, children explored both 2-dimensional and 3-dimensional shapes in a variety of tactile, kinesthetic, and visual ways.” 

The instructional materials relate grade-level concepts with work in future grades. Each Section Organizer contains a Coherence section with “Links to the Future”. This section identifies what students “will do in the future.” Examples include:

  • Teacher’s Lesson Guide, Section 1 Organizer, Coherence, “Links to the Future” for K.CC.1, “Children will continue to extend their knowledge of the count sequence across the year through a variety of oral counting activities and as they count objects in sets of increasing sizes. They will learn to count by 10s beginning in Section 4. In Grade 1, they will extend their knowledge of the oral count sequence to at least 120.”
  • Teacher’s Lesson Guide, Section 2 Organizer, Coherence, “Links to the Future” for K.OA.2, “Throughout the year, children will solve addition and subtraction problems within 10 in a variety of contexts, including number stories, domino and dice games, as well as other activities. In Grade 1, children will model and solve problems involving addition or subtraction of two numbers within 20.”
  • Teacher’s Lesson Guide, Section 4 Organizer, Coherence, “Links to the Future” for K.MD.1, “In Kindergarten Sections 4 through 9, children will practice observing and describing an object's length, weight, and capacity, as well as describing several measurable attributes of a single object. In Grade 1, children will quantify length measurements as the number of same-size units that span a distance.”
  • Teacher’s Lesson Guide, Section 5 Organizer, Coherence, “Links to the Future” for K.NBT.1, “In Section 5, children compose and decompose numbers 11 through 19 on double ten frames and with partners using two pairs of hands. In Sections 7 and 8, they record these types of decompositions with drawings and equations. In Grade 1, children will apply this concept as they extend their understanding of place value to include all 2-digit numbers.”
  • Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Future” for K.G.3, “In Section 6, children learn the difference between 2- and 3-dimensional shapes as they assemble and analyze objects for the Solid-Shapes Museum, and stamp different 2-dimensional faces of 3-dimensional shapes onto paper. They will continue to explore and compare 2-D and 3-D shapes, and the relationships between them, as they play Solid-Shapes Match Up in Section 7 and as they create both 2-D and 3-D shapes from marshmallows and toothpicks in Section 8.”

In some lessons, the instructional materials contain content from future grades that is not clearly identified as such. Examples include:

  • Lesson 4-3, Focus: Graphing Favorite Colors, “Model how to label the axes on the graph with the color names and a number of children who chose the color as their favorite. Explain that this is sometimes called a bar graph, and ask why it might have that name.” Students can choose from 6 colors, making 6 categories on the graph. This lesson is labeled K.MD.3, “Classify objects into given categories; count the number of objects in each category and sort the categories by count.” Using a bar graph with up to three categories is a Grade 1 standard (1.MD.4, “Organize, represent, and interpret data with up to three categories…”)
  • In Lesson 5-6, Practice: Solving Number Stories, students solve problems in their journals. Sample problem, “I saw some children swinging. One more child joined them. Then there were 9 children swinging. How many children were swinging at the beginning?” This lesson is labeled K.CC.5, “Count to answer ‘how many’ questions.” Starting with an unknown in a problem-solving situation is a Grade 1 standard (1.OA.1, “Use addition and subtraction within 20 to solve word problems with unknowns in all positions”).
  • In Lesson 5-9, Focus: Introducing the Equal Symbol, students use their fingers to show different representations of the numbers 3, 4, and 5. The teacher is instructed to “Introduce the word equal as a way to describe two quantities that are the same. Explain that there is also a symbol that means equal. Write the word equal, draw the equal symbol on the board, and have children make the symbol using two fingers on opposite hands. Explain that this means that the total on both sides of the symbol is the same: 5 is equal to 5. Mention that another way to say equal symbol is equal sign.” This lesson is labeled as K.CC.5, “Count to answer ‘how many’ questions”; 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”; and K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.” Understanding the meaning of the equal sign and determining if equations involving addition and subtraction are true or false is aligned to a Grade 1 standard (1.OA.7, “Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false”).
  • In Lesson 9-4, Focus: Measuring and Comparing Backpacks, students use connecting cubes to measure the height and width of their backpack and that of a partner. The teacher is prompted to, “introduce the term area as the amount of flat space that is taken up by the front, the back surface, or side, of the backpack. Explain that children can trace the outline of a backpack on large paper to help them see and compare the area of one side. Ask: Which backpack takes up more space (has a larger area)?” This lesson is labeled K.MD.1, “Describe measurable attributes of objects such as length or weight.” Recognizing area as an attribute of plane figures and understand concepts of area measurement is a Grade 3 standard (3.MD.5, “Recognize area as an attribute of plane figures and understand concepts of area measurement”).

The instructional materials do not present sufficient opportunities to meet the full intent of standards K.NBT.1 and K.G.5. Examples include:

  • K.NBT.1, “Compose and decompose numbers from 11 to 19 into ten ones and some further ones,” is addressed in the Focus section of Lessons of 5-6, 5-8, 7-3, 8-6, and 8-13. K.NBT.1 is also embedded in Routine 1: Number of the Day, where students track the number of days in school on a Growing Number Line, and represent the number of the day with objects. These opportunities are not sufficient for students to meet the full intent of K.NBT.1.
  • K.G.5, “Model shapes in the world by building shapes from components,” is taught in the Focus section of lessons 3-3, 5-4, 8-2, 9-7, 9-12, and 9-13.

Indicator 1f

Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
2/2
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings. Focus and Supporting Clusters addressed in each section are found in the Table of Contents, the Focus portion of each Section Organizer, and in the Focus portion of each lesson. Examples include:

  • Lesson 1-9, Focus: Representing 5 is shaped by K.OA.A, “Understand addition as putting together and adding to, and subtraction as taking apart and taking from.” The featured number of the day is 5. Students show different ways to represent 5.
  • Lesson 2-8, Focus: Getting to Know Circles is shaped by K.G.A, “Identify and describe shapes.” Students look at a circle and describe its attributes; they then look around the room to find other circles.
  • Lesson 5-1, Focus: Celebrating the 100th Day is shaped by K.CC.A, “Know number names and the count sequence.” Students share and compare the collections of 100 they brought to school.
  • Lesson 6-2, Focus: Ordering Straws by Length is shaped by K.MD.A, “Describe and compare measurable attributes.” Students work with a partner to order a set of 5 straws by length.
  • Lesson 8-6, Focus: Bundling Craft Sticks is shaped by K.NBT.A, “Work with numbers 11-19 to gain foundations for place value.” Students take 15 craft sticks and bundle them into a group of 10 and a leftover group of 5.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:

  • In Lesson 1-8, Focus: Making an Age Graph, students practice counting the number of students in different age groups and then discuss which line has more and less people. K.CC.A, “Know number names and the count sequence” is connected to K.CC.C, “Compare numbers.” 
  • In Lesson 2-9, Focus: Exploring Ten Frames, students represent 10 and 5 counters on a ten frame and share their representations. K.CC.B, “Count to tell the number of objects” is connected to K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
  • In Lesson 2-12, Practice: Revisiting Shape Collages, students sort shape cards onto the proper collage and describe their sorting attributes. Cluster K.G.A, “Identify and describe shapes” is connected to K.G.B, “Analyze, compare, create, and compose shapes.”
  • In Lesson 3-2, Focus: Finding Combinations of Ten, students use two-colored beans to fill in a ten frame, and then color a ten frame to match the combination. K.CC.B, “Count to tell the number of objects” is connected to K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
  • In Lesson 4-1, Focus: Exploring Attribute Blocks, students work in groups to describe the blocks and then sort them. Cluster K.MD.A, “Describe and compare measurable attributes” is connected to K.MD.B, “Classify objects and count the number of objects in each category.”
  • In Lesson 5-8, Focus: Playing Teens on Double Ten Frames, students take turns spinning on a 10-20 Spinner and placing the number of counters on their double ten frame. Students compare their double ten frames and the student with the largest number wins the round.  K.CC.C, “Compare numbers” is connected to K.NBT.A, “Work with numbers 11-19 to gain foundations for place value.” 
  • In Lesson 6-9, Focus: Playing Disappearing Train, students roll a subtraction die marked with -1, -2, and -3. Students roll the die and use a snap cube train to take away the matching number of cubes. K.CC.B, “Count to tell the number of objects” is connected to K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”
  • In Lesson 8-2, Focus: Modeling Shapes, students create 2-D and 3-D shapes with toothpicks and marshmallows. K.G.B, “Analyze, compare, create, and compose shapes” is connected to K.MD.A, “Describe and compare measurable attributes.”

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

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Gateway Two Details

The instructional materials for Everyday Mathematics 4 Kindergarten partially meet expectations for Gateway 2, rigor and the Mathematical Practices. The instructional materials meet expectations for rigor, attending to procedural skill and fluency and conceptual understanding, and they do not always treat the three aspects of rigor together or separately. The instructional materials identify and use the Mathematical Practices (MPs) to enrich grade-level content, but do not provide students with opportunities to meet the full intent of all MPs. The instructional materials meet expectations for students constructing viable arguments and analyzing the arguments of others and also for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of others. The instructional materials partially attend to the specialized language of mathematics.

Criterion 2a - 2d

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.
7/8
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Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for rigor and balance. The materials attend to procedural skill and fluency and conceptual understanding, and they partially attend to application. The materials do not always treat the three aspects of rigor together or separately.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding throughout the grade level. The Focus portion of the lesson provides opportunities for students to explore, engage in, and discuss conceptual understanding of mathematical content. Examples include:

  • In Lesson 1-10, Focus: Introducing Quick Looks, “Present the dot images in order from Cards 1 to 10. Flash each image and ask: ‘What did you see/How did you see it?’ To move children beyond counting, highlight strategies that involve decomposing the number by asking questions such as: ‘Did everyone understand Tamika’s strategy of seeing groups? Can someone say it for us again? Can you try her way on the next card?’” This activity supports conceptual understanding of K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way” and K.CC.4, “Understand the relationship between numbers and quantities.”
  • In Lesson 2-5, Focus: Solving Pocket Problems, each student has ten counters to help them solve pocket problems. The teacher demonstrates by putting three counters in the pocket. Then the teacher shows one more counter and adds it to the pocket. Students use their counters to show how many are in the pocket now. The teacher then takes all the objects out of the pocket and leads the class in counting the total. After practicing as a class adding to or taking away from the pocket, students work in pairs giving each other pocket problems. This activity supports conceptual understanding of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, or sounds.”
  • In Lesson 4-8, Focus: Decomposing Numbers, “Children use connecting cubes to compose and decompose numbers in multiple ways.” At the conclusion of the lesson, students share their results, and the teacher asks, “What did you notice? Did you see any patterns?” leading to the concepts of turnaround pairs and doubles. This activity supports conceptual understanding of K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.”
  • In Lesson 5-5, Focus: Representing Teen Numbers, “Hold up the 10 card from the Class Number Card set and have all children hold up 10 fingers. Ask: What number comes next? Hold up the 11 card and ask if anyone can think of a way to show 11 fingers. If no one suggests it, call on two children to work together. Choose one child to hold up all 10 fingers. Ask the other child how many fingers he or she must hold up so that together they show 11 fingers. Repeat with the number 15, having one child show 10 fingers and another child show 5 fingers.” This activity supports conceptual understanding of K.NBT.1, “Compose and decompose numbers from 11 to 19 into ten ones and some further ones.”
  • In Lesson 7-9, Focus: Exploring Number Combinations, “Model how to make a counting loop by placing beads on a chenille stem and twisting (or tying) the ends together to close and fasten the loop. Have each child take one chenille stem, put 7 to 9 same-color beads on it, and make a loop. (Children will make bead combinations that add to 10 in Lesson 8-9, Practice.) Direct them to group their beads and write number sentences for four different groupings on the ‘My First Math Book’ page. Challenge children to divide their beads into three groups for the last box on the page.” This activity supports students’ conceptual understanding of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.”

Games, Daily Routines, and Math Masters provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

  • In Routine 1: Number of the Day, “Use think aloud to briefly review the total days in terms of tens and ones: first count the bundles of tens and then count the ones. Confirm that the total number of straws or sticks matches the number of days in school so far.” The teacher asks, “How many days have we been in school? How is this shown on the Class Number Line? How is it shown by the straws (or sticks or whatever material your class uses) in our Concrete Number Count?” This activity provides continuous conceptual understanding practice of K.OA.1, “Represent addition and subtraction with objects.”
  • In Lesson 1-3, Game: Gotcha, students use one-to-one correspondence and the cardinal principle as they engage in a counting game. In this game, students “catch” the teacher making counting mistakes such as “saying the number words in the wrong order, not saying one number word for each object the teacher points to, and saying the wrong number for the total of the set (for example 1, 2, 3, 4; that’s 3 objects!).” Students signal with a “thumbs up” if the teacher is counting correctly and switch to “thumbs down” when the teacher makes a mistake. Each time the teacher makes an error, the students explain the mistake and model the correct counting. This activity provides practice of conceptual understanding of K.CC.4a, “When counting objects, say the number names in standard order, pairing each object with one and only one number name and each number name with one and only one object” and K.CC.4b, “Understand that the last number name tells the number of objects counted.”
  • In Lesson 2-4, Math Masters, students independently use counters and a blank number board to cover the spaces on their board with the appropriate number of objects. This supports conceptual understanding of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”
  • In Lesson 3-2, Math Masters, students toss 10 pennies and sort into groups of “heads” and “tails” and put them on a ten frame. Then they count the number of heads and tails and record the numbers. This activity is repeated three more times and supports the conceptual understanding of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”
  • In Lesson 5-10, Math Masters, students take turns with a family member telling and solving number stories that use addition. They are encouraged to use pennies or other small objects, and the addition symbol to act out or model their stories. This activity supports the conceptual understanding of K.OA.1, “Represent addition with objects, fingers, acting out, or equations.”

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade level. The Section Organizer provides information on which part of each lesson develops procedural skill and fluency. Opportunities are found in the Daily Routines, Focus, and Practice portions of the lesson. Examples include:

  • In Lesson 6-11, Practice: Counting to the Number of the Day, “First have children choral count by 1s to the Number of the Day. To practice counting on from different numbers, stop children during the sequence; then skip to a new number and have them restart. Next have children count by 10s and then 1s to the Number of the Day (10, 20, 30, 40, 50, 60, 61, 62…). Encourage children to use the number line to help them count if needed.” This activity provides an opportunity for students to develop fluency of K.CC.1, “Count to 100 by ones and by tens,” and K.CC.2, “Count forward beginning from a given number within the known sequence (instead of having to begin at 1).”
  • In Lesson 7-12, Focus: Playing Dice Addition, students play with a partner and each roll a set of the Addition Dice. Once they roll their dice they state the resulting addition equations such as, “2 + 3 = 5.” The student with the higher total colors a square on their ten frame, and the first student to color all ten spaces wins. This activity provides an opportunity for students to develop fluency of K.OA.5, “Fluently add and subtract within 5.”
  • In Lesson 8-11, Focus: Playing Addition Top-It, students play with a partner and each take two cards from the top of the deck and place them faceup. Then they add the two numbers and state their total. The player with the higher total takes all 4 cards and the player with the most cards at the end wins. This activity provides an opportunity for students to develop fluency of K.OA.5, ”Fluently add and subtract within 5.”
  • In Routine 5: Survey, each week the teacher poses a survey question and students record their responses. Teachers choose how students record their answers. They can use a magnet and place it in the appropriate column, designate colored cubes for responses and students choose the cube that corresponds to their response, or students write their initials in the column on chart paper corresponding to their response. Once all responses are collected, the teacher appoints a Survey Helper to lead the class in counting and recording the results. This weekly activity provides an opportunity for students to develop fluency of K.CC.1, “Count to 100 by ones and by tens,” and K.CC.3, “Write numbers from 0 to 20.”
  • In Routine 3: Daily Schedule and Monthly Calendar Routine, at the end of the month students take down the calendar in preparation for the next month. Dismantling the Calendar states, “Dismantling the calendar is a rich whole-class activity that provides an opportunity to enhance number skills and awareness of calendar patterns.” Teacher prompts change in complexity as the year progresses. For example, students are prompted to, “Remove or erase the number that equals 2 + 5. Remove or erase all pairs of date numbers that add to 7, or remove or erase two date numbers that add to 10.” This monthly activity provides an opportunity for students to develop fluency of K.OA.5, “Fluently add and subtract within 5,” and K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.”

The instructional materials provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade level. The Section Organizer provides information on which part of each lesson develops procedural skill and fluency. Opportunities are found in the Practice portions of the lesson and the Math Masters. The materials provide only partner or group activities for fluency of K.CC.2, “Count forward beginning from a given number,” and independent opportunities are only found in assessments. Examples include:

  • In Lesson 5-11, Math Masters, students cut out an addition symbol, then they put some snacks, like goldfish, on the table and count them. Then students put another group of snacks on the other side of the addition symbol. Finally, students remove the addition symbol, put all of the snacks together and count to find out how many. This activity is repeated several times and provides an opportunity for students to independently demonstrate the procedural skill of K.CC.5, “Count to answer ‘how many’ questions about as many as 20.”
  • In Lesson 7-7, Practice: Playing Roll and Record with Dot Dice, students roll a set of dice, determine the sum and write number sentences on slates such as, “3 + 2 = 5”. This activity provides an opportunity for students to develop fluency of K.OA.5, “Fluently add and subtract within 5.”
  • In Lesson 8-12, Math Masters, students roll two die, determine their total, and then record the total on the Roll and Record Grid. This activity provides an opportunity for students to develop fluency of K.OA.5, “Fluently add and subtract within 5.”
  • In Lesson 9-3, Practice: Counting the Class Collection, students count the items in the class collection using groups or counting-on strategies and record in their My First Math Book. The teacher asks, “What do you notice about the number of ___ in our collection since we started it? Where was the largest jump in our total? Can you see it on the table? On the thermometer display? What else do you notice about the data and the displays? This activity provides an opportunity for students to independently demonstrate procedural skill of K.CC.3, “Write numbers from 0 to 20,” K.CC.5, “Count to answer how many questions,” and K.CC.7, “Compare 2 numbers between 1 and 10 presented as written numerals.”

Indicator 2c

Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The materials do not provide opportunities for students to independently engage in non-routine applications of mathematics throughout the grade level.

Examples of students engaging in routine application of mathematics include:

  • In Lesson 2-12, Focus: Telling and Acting out Number Stories, students solve change-to-more, change-to-less, and parts-and-total problems. Students can act out each story, use counters or their fingers, or use drawings to model the story as the teacher tells it. For example, “Davon was snack helper today. He carried 3 apples to the table. Then he got 2 more apples. How many apples does Davon have now?” Students apply their understanding of K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”
  • In Lesson 3-8, Focus: Playing Spin a Number, students spin a spinner and move their counter that number of spaces on the playing board by reading the number counting aloud. Students apply their understanding of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality.”
  • In Lesson 5-3, Focus: Playing Ten Bears on a Bus, students play the game Ten Bears on a Bus to generate number combinations that add to 10. For example, “4 yellow bears are on the bus, how many red bears must get on the bus to fill all 10 seats?” Students apply their understanding of K.OA.3, “Decompose numbers less than or equal to 10 into pairs in more than one way.”
  • In Lesson 5-10, Focus: Using the Addition Symbol, students use a craft stick with an addition symbol written on it and counters to model and solve change-to-more, parts-and-total, and total-unknown problems. For example, “Sasha saw 3 squirrels climb the tree. 3 more climbed up to join them. How many squirrels are in the tree now?” Students apply their understanding of K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”
  • In Lesson 8-8, Playing Car Race, students work cooperatively to move counters to the 10 space on the gameboard by rolling a die. While moving their counter forward, they must roll a number that exactly lands them on the ten space. Students apply their understanding of K.OA.4, “For any number from 1 to 9, find the number that makes 10 when added to the given number.”

The materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. Examples include:

  • In Lesson 5-4, Focus: Finding and Drawing Shapes, My First Math Book, students independently draw four shapes they see in a picture shown by the teacher. This activity provides the opportunity for students to independently demonstrate K.G.5, “Analyze, compare, create, and compose shapes.”
  • In Lesson 5-7, Focus: Solving the Open Response Problem, students solve, “I was having a party. I put 4 chairs at the table. The doorbell rang, and I saw 7 friends at the door. Do I have enough chairs for all my friends? How do you know?” This activity provides the opportunity for students to independently demonstrate K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”
  • In Lesson 6-7, Focus: Solving the Open Response Problem, teachers present the following situation: “I went to an amusement park, and there was a ride with a sign that said, ‘You must be as tall as this sign to ride.’ I wondered if any of you would be tall enough to ride, but the sign did not have any numbers or measurements on it. I needed a way to remember and describe how tall the sign was. I did not have any string, but I found some stick-on notes in my bag and used them to measure the sign. It was as tall as 12 stick-on notes!” Students use stick-on notes to determine how tall they are and if they are able to ride. Results and solutions are recorded on Math Masters page 90. This activity provides the opportunity for students to independently demonstrate K.MD.2, “Directly compare two objects with a measurable attribute in common, to see which object has ‘more of’ or ‘less of’ the attribute, and describe the difference.”
  • In Lesson 6-9, Focus: Playing Disappearing Train, students play Disappearing Train with a partner. They roll a die marked with (-1, -2, and -3) meaning “take away”. The die tells students how many cars to take away/subtract from their train during a turn. Teachers model, “I had 12 cars. I subtracted 2 cars. Now I have 10 cars. My train is shorter than your train.” This activity provides the opportunity for students to independently demonstrate K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”

Indicator 2d

Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently throughout the program materials. 

The materials attend to conceptual understanding. Examples include:

  • In Lesson 5-8, Focus: Playing Teens on Double Ten Frames, “Distribute a blank double ten frame to each child. Discuss what children notice about it, making connections to the ten frames they have used before. Hold up a number card between 10 and 19 and ask children to use counters to show that number on their double ten frame. Direct children to fill one ten frame first (ten ones, or the ten) and then add counters to the second ten frame to complete the number.” This activity helps develop conceptual understanding of K.NBT.1, “Compose and decompose numbers 11 through 19 into ten ones and some further ones.”
  • In Lesson 8-5, Focus: Playing Dice Subtraction, each student is given a blank ten frame and a pair of Dice Subtraction dice. Students take turns rolling the dice and subtracting the smaller number from the larger number, then state the subtraction equation and the difference to their partner. The student with the smallest difference colors one space on their ten frame. The winner is the student who fills their ten frame first. This activity develops conceptual understanding of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, sounds, acting out situations, verbal explanations, expressions, or equations.”

The materials attend to procedural skill and fluency. Examples include:

  • In Lesson 4-2, Practice: Playing Roll and Record, students play a dice game using a Roll and Record Grid. Students roll the dice and fill in the grid to see what number gets filled first, or students can play with a partner to see who gets their number filled on the grid first. This develops the procedural skill of K.CC.5, “Count to answer ‘how many’ questions about as many as 20 things.”
  • In Lesson 8-11, Focus: Playing Addition Top-It, students play with a partner using a deck of cards. Each player takes 2 cards, lays them faceup, and adds the 2 numbers stating their total. The students with the greater total takes all 4 cards. The player with the most cards wins. This develops the procedural skill and fluency of K.OA.5, “Fluently add and subtract within 5.”

The materials attend to application. Examples include: 

  • In Lesson 4-13, Practice: Comparing Capacities, students are shown various containers of different sizes filled with beans or other pourable materials, and a reference container. The materials state, “Have a child choose one. Ask: Do you think this container holds more or less than the mug? How can we find out? As needed, model pouring the beans from the mug into the other container to compare capacities. Have children work in a small group to compare various containers to the reference container.” This activity provides the opportunity to apply the understanding of K.MD.2, “Directly compare 2 objects with a measurable attribute in common to see which object has more or less of the attribute.”
  • In Lesson 6-8, Practice: Using the Subtraction Symbol, students use a craft stick, a sheet of paper, and about 10 counters to model subtraction story problems, “Levi saw 5 birds. Three birds were red. The rest were orange. How many birds were orange.” Students write a “-” symbol on their craft sticks and model the number stories with the craft sticks and counters. As they model, they discuss how to write the number models for the stories. This activity provides the opportunity to apply the understanding of K.OA.2, “Solve addition and subtraction word problems, and add and subtract within 10.”

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

  • In Lesson 4-3, Focus: Favorite Colors Graph, students group themselves according to their favorite colors and create a graph to represent and analyze the results. After students create a Favorite Colors Graph, the teacher leads a class discussion analyzing and making comparisons of the graphs, “How many more children chose red than green? How did you figure that out?” Students practice fluency of K.CC.5, “Count to answer ‘how many’ questions about as many as 20 things,” and application of K.MD.3, “Classify objects into given categories, count the number of objects in each category and sort the categories by count.”
  • In Lesson 4-6, Focus: Counting and Moving with Teens, students use a number line to extend the counting sequence beyond 10 to include teen numbers. Students are asked, “What is the same about these numbers? How are they different from the numbers 1 through 9? Why do you think they are called teen numbers?” Students then read numbers from 10-19 Class Number cards. Students develop conceptual understanding of K.CC.4, “Understand the relationship between numbers and quantities; connect counting to cardinality,” and fluency of K.CC.A, “Know number names and the count sequence.”
  • In Lesson 8-13, Focus: Making Name-Collection Posters, the teacher writes the number 10 at the top of chart paper and draws a filled in ten frame and writes 5 = 5 on the paper. Students are asked to share other ways to show or name 10 and the teacher adds their responses. Students develop conceptual understanding of K.OA.A, “Understand addition as putting together and adding to, and subtraction as taking apart and taking from,” while applying understanding of K.NBT.1, “Compose and decompose numbers from 11 to 19.”

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
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Criterion Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten partially meet expectations for practice-content connections. The instructional materials identify and use the Mathematical Practices (MPs) to enrich grade-level content, but do not provide students with opportunities to meet the full intent of MP5, choose tools strategically. The instructional materials meet expectations for students constructing viable arguments and analyzing the arguments of others and also for assisting teachers to engage students in constructing viable arguments and analyzing the arguments of othersThe instructional materials partially attend to the specialized language of mathematics.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade level.

All MPs are clearly identified throughout the materials, with few or no exceptions. Examples include:

  • The mathematical practices are listed on pages xi-xiii in the Kindergarten Volume I Teacher’s Lesson Guide as “Correlation to the Mathematical Process and Practices” which states, “Everyday Mathematics is a standards-based curriculum engineered to focus on specific mathematical content, processes, and practices in every lesson and activity. The chart below shows complete coverage of each mathematical process and practice in the core program throughout the grade level.” 
  • Each Section Organizer contains a Mathematical Background: Processes and Practices component identifying the MPs addressed in the section and in individual lessons. Additionally, “The authors created Goals for Mathematical Practice (GMP) that unpack the practice standards, operationalizing them in ways that are appropriate for elementary students.” 
  • Within each lesson description, GMPs appear in bold print and teacher side notes identify the MPs that are addressed in the lesson.

The majority of the time the MPs are used to enrich the mathematical content. Examples include:

  • In Lesson 1-10, Focus: Introducing Quick Looks, “Present the dot images in order from Cards 1 to 10. Flash each image and ask: What did you see? How did you see it? To move children beyond counting, highlight strategies that involve decomposing the number by asking questions such as: Did everyone understand Tamika’s strategy of seeing groups? Can someone say it for us again? Can you try her way on the next card?” The mathematical content in this activity is enriched by MP1.
  • In Lesson 2-11, Focus: Getting to Know Rectangles, students are shown shape cards of several rectangles to look for similarities and differences. Teachers ask, “How are all these rectangles alike? How are all these rectangles different from one another? How can all these shapes be rectangles when they look different from one another? and What other shapes have we learned about that have lots of different types?” The mathematical content in this activity is enriched by MP7.
  • In Lesson 6-6, Focus: Playing “What’s My Rule?” Fishing, students try to figure out what rule the teacher is applying as they fish and catch students (wearing red). Teachers ask, “What is the same about the fish I caught? What is the same about the fish who are not in my net? If I continue to follow my rule, who else can I catch? Why? and Can you state my sorting rule?” The mathematical content in this activity is enriched by MP8.
  • In Lesson 6-13, Focus: Relating Symbols to Number Stories, students make sense of “join” or “take away” word problems. For example, “I have 5 stickers, 3 are red and the rest are yellow. How many stickers do I have?” In their My First Math Book on page 10, students draw or write one join and one take-away number story and use a number model to represent the story. The mathematical content in this activity is enriched by MP4.
  • In Lesson 8-6, Focus: Bundling Craft Sticks, students work in pairs to estimate the number of sticks in a bag (10 - 19). Students then bundle the sticks into 10 sticks and some more sticks. For example, “Have children bundle the sticks into groups of 10 and re-count the sticks by 10s and 1s. Model how to record their findings by showing the number as 10 and some 1s, on a double ten frame, and as an equation.” The mathematical content in this activity is enriched by MP2.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten partially meet expectations for carefully attending to the full meaning of each practice standard. The materials attend to the full meaning of most of the MPs, but they do not attend to the full meaning of MP5 as students do not get to choose tools strategically.

Examples of the materials attending to the full meaning of most MPs include:

  • MP1: In Lesson 9-12, Focus: Preparing for a Math Celebration, students determine how many chairs, tables, napkins, plates, utensils, and food items are needed for the party using a list of expected guests.
  • MP2: In Lesson 6-8, Focus: Using the Subtraction Symbol, students write the subtraction symbol on a craft stick. They then model subtraction stories using the craft stick and counters. The lesson concludes with students making and sharing their own number stories involving subtraction for the class to model and solve.
  • MP4: In Lesson 2-12, Focus: Telling and Acting Out Number Stories, students solve number stories such as, “Davon was snack helper today. He carried 3 apples to the table. Then he got 2 more apples. How many apples does Davon have now?” through modeling. They are encouraged to use counters, fingers, drawings, or act out the situation to solve. 
  • MP6: In Lesson 5-9, Focus: Introducing the Equal Symbol, “Group children into pairs and give each child a craft stick and ten counters. Show children how to arrange their craft sticks horizontally, one above the other, to create an equal symbol. Have one child place a set of counters on one side of the equal symbol and the other child create an equal set (grouped differently, if they are ready) on the other side. Encourage children to describe their equations (for example: two equals two; six equals three red and three blue).”
  • MP7: In Lesson 8-7, Focus: Solving the Open Response Problem, “Tell children that on the way to school today, you saw the same 2 wires, but this time there were 10 birds flying nearby! Explain that they will work in pairs to find as many different ways as they can to show 10 birds sitting on 2 wires. Encourage them to record their combinations in a way that makes sense to them and that others can see and understand such as sketches, number pairs, or number sentences.
  • MP8: In Lesson 2-7, Focus: Solving the Open Response Problem, students sort and classify objects, “Give each pair a sorting mat and a collection of objects. As children work, circulate and provide support and guidance for sharing objects and working together, as well as for sorting. Ask questions such as: How would you describe this group of objects you created? What is your rule for sorting your objects?”

Examples of the materials not attending to the full meaning of MP5 because students do not get to choose tools strategically include:

  • In Lesson 4-4, Focus: Exploring Calculators, students are given calculators to display their answer to questions such as, “How many legs are on your chair? How many fingers do you have on one hand? and How many days are in one week?” 
  • In Lesson 6-1, Focus: Comparing Body Heights to Objects, “Explain that children will use string to compare their body heights with classroom objects.” 
  • In Lesson 9-5, Focus: Measuring and Comparing Backpacks, students compare the capacity and weight of backpacks, “Pair children with their partners from Lesson 9-4 to compare the weights and capacities of their backpacks. First have children act as human pan balances to compare the weights of the backpacks by feel. Then have them use a scale if one is available. Next have children determine the total number of books that can fit in each backpack.”

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Student materials consistently prompt students to construct viable arguments and analyze the arguments of others. Lessons offer Differentiated Options where students work in small groups or with partners as teachers facilitate discussions so students have opportunities to construct viable arguments and critique the reasoning of others. Open Response and Reengagement Lessons provide opportunities for students to critique the open response answers of other students. 

Students construct arguments. Examples include:

  • In Lesson 4-2, Focus: Identifying Attributes of Shapes, “Introduce the Feely Box and note that there are different shapes inside the box that children will touch but not see. Explain that you will give clues to help them choose shapes from the box, and they will then explain why they chose the shape. Select from the activities below, choosing prompts that are best suited to children’s skill levels.” Two of the possible activities state, “Have a child pick out two shapes that feel the same. Have the child show the shapes to the class and name them. Ask: How do you know that the shapes were the same? Name a shape and have a child find it by touch. Ask: How do you know you found a _____?”
  • In Lesson 5-2, students play a game of Roll & Record. After the game, a class chart is made recording each child’s winning number. Students analyze the results of the game and respond to questions, “Why did the middle numbers win most often? How many ways are there to get 2? Are there more ways to get 8? Why?”
  • In Lesson 5-7, Focus: Solving the Open Response Problem, teachers pose the following question, “There were 6 coats hanging on hooks. Two children put on their coats. I think there are 4 coats still hanging on hooks. Am I right? How do you know?” Teachers explain that two students tried to solve the problem and display Child 1’s solution and ask, “Does this child think there are 4 coats left on hooks? How can you tell? Sample answer: Yes. The child drew 4 coats hanging on hooks and said ‘Yes’ on his or her paper.”

Students critique the reasoning of others. Examples include:

  • In Lesson 3-12, Practice: Solving Number Stories, “After they have a chance to solve each problem, invite children to share and discuss how they solved them. Elicit a variety of different approaches such as counters, drawing pictures, counting, and using derived facts. Have children show and compare their various methods, rather than just describe them.”
  • In Lesson 8-7, Focus: Reengaging in the Problem, students answer an open response problem about Birds on Wires. The materials state, “Review the Birds on Wires open response problem. Tell children that today they will look at different ways some of them solved the problem. Begin by showing some correct and incorrect solutions you found in their work. Prompt children to describe and compare the two solutions by asking: Can both of these solutions be correct? Why or why not? How can we figure out the number of birds on the second wire if we have 4 birds on the first wire? Does the number of birds drawn on each wire match the numbers below it?”
  • In Lesson 9-1, Focus: Playing Make My Design, students play a partner game where one student creates a design with pattern blocks, then uses shape and positional language to describe the design to the other partner. The materials state, “Encourage the other partner to try to re-create the design from the instructions, asking for further description and clarification as needed.”

Indicator 2g.ii

Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Examples of assisting teachers in engaging students to construct viable arguments include:

  • In Section 5 Organizer, Mathematical Background: Process and Practice, Standard for Mathematical Process and Practice 3, “Children have been informally “justifying their conclusions and communicating them to others” all year. In Section 5, children have opportunities to ‘construct arguments using concrete referents such as objects, drawings, diagrams, and actions.’ For example, when graphing sums of dice rolls (Lessons 5-2 and 5-7), children explain why they think there are more combinations for some totals than for others and use examples from their recording sheets to justify their explanations. Children also make a mathematical argument in the Lesson 5-7 Open Response task as they explain and justify their solution to a number story. As they work with Shape Cards (Lesson 5-13), children ‘make conjectures’ about how to combine shapes to make new shapes.”
  • In Lesson 4-9, Differentiation Options, Extra Practice, Predicting and Testing Weights, “To provide additional practice comparing and describing the weights of objects, encourage children to predict which of the two objects is heavier and which one is lighter. Have them explain their reasoning and then use a pan balance to test their predictions.”
  • In Lesson 7-4, Focus: Playing Solid-Shapes Match Up, “Show children an object from the Solid-Shapes Museum, and invite them to name the object (sphere or cone, for example) and describe it in detail. Ask whether the object is 2- or 3-dimensional, and prompt children to explain their thinking. Review and discuss the definitions of these terms as needed. You might review the comparisons they made in lesson 6-5 (between a circle and a sphere, and a square and a cube) to illustrate that 2-dimensional (or 2-D) shapes are flat and 3-dimensional (or 3-D) shapes are not.”

Examples of assisting teachers in engaging students to analyze the arguments of others include:

  • In Lesson 3-12, Practice: Solving Number Stories, students solve a variety of number stories such as, “There were 6 apples in the bowl. Carlos took 3 of the apples. How many apples were left in the bowl?” Teachers are prompted, “Provide children with counters and writing materials. After they have a chance to solve each problem, invite children to share and discuss how they solved them. Elicit a variety of different approaches, such as using counters, drawing pictures, counting, and using derived facts. Have children show and compare their various methods, rather than just describe them.”
  • In Lesson 5-7, Focus: Solving the Open Response Problem, “Explain that you are going to share how two children solved this problem and justified, or tried to ‘prove’, their answers. Display Child 1’s solution from the top of Math Masters, p.81, and read the dictation under the drawing: Yes, I knew it in my brain. Ask: Does this child think there are 4 coats left on hooks? How can you tell? Does this child show the whole story?”
  • In Lesson 8-13, Focus: Making Name-Collection Posters, students make posters to represent equivalent names for a number between 5 and 20. At the conclusion of the activity, teachers are directed, “Have groups share their posters. Help other children make sense of each poster by asking questions such as: Which names for 10 did you recognize quickly? Which ones are harder to figure out? Why? Did this group represent their number in a way that you didn’t use for your name collection? If time permits, allow groups to revisit their posters and add new representations they learned as a result of sharing.”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
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Indicator Rating Details

The instructional materials reviewed for Everyday Mathematics 4 Kindergarten partially meet expectations for explicitly attending to the specialized language of mathematics. The materials provide explicit instruction on how to communicate mathematical thinking using words, diagrams, and symbols, but there are instances when the materials use mathematical language that is not precise or appropriate for the grade level.

 

The Section Organizer provides a vocabulary list of words to be used throughout lesson discussions. Each lesson contains a vocabulary list, Terms to Use, and vocabulary words appear in bold print in the teacher notes. Some lessons incorporate an Academic Language Development component that provides extra support for the teacher and students. Additionally, the Teacher’s Lesson Guide contains a detailed glossary with definitions and images where appropriate. Examples of explicit instruction on how to communicate mathematical thinking include:

 

  • In Lesson 1-12, Focus: Describing and Comparing Shapes, students are shown Shape Cards and describe them. The teacher prompt states, “As children share, make a list of the descriptive terms they use, adding quick sketches to illustrate each term. Probe to elicit terms such as curve/curvy, round, straight, line, side, corner, pointy, fat, wide, narrow, open, and closed. Think aloud to model detailed descriptions. For example, you might say: I noticed this shape is round here, but straight here. Together create a list of terms that children can use now and in the future to describe shapes in detail. Gradually you will build from children’s natural, informal language to introduce more formal terms such as vertex and angle.” 
  • In Lesson 2-3, Focus: Getting To Know Triangles, “Display the large posterboard triangle you created and ask children to repeat the name of the shape: triangle. Place the triangle where children can look at it and have them draw your triangle in the air with large arm motions, saying side, vertex, side, vertex, side, vertex as they draw. Ask children to describe the triangle. If needed, prompt them with these questions: How many sides does this triangle have? How many vertices (corners) does it have? Are the sides straight or curved? Emphasize that triangles have three straight sides and three vertices (corners).”
  • In Lesson 7-6, Focus: Balancing Objects with Clay, teachers display a pan balance, “Ask children to share words they use to describe weight and when they talk about weight in their everyday lives. Prompt with questions such as: How is weight different from length or height? Can you think of something that is very heavy? Can you think of something that is very light?” 
  • In Lesson 8-5, Focus: Playing Dice Subtraction, “Tell children that today they will play a game called Dice Subtraction that will give them practice subtracting small numbers quickly to find the difference between them. Explain that difference means the result, or answer, you get when you subtract one number from another. You may also wish to model and explain that the difference is the distance (or number of ‘hops’) between two numbers on a number line. (For example, the difference, or distance, between 5 and 2 on the number line is 3 ‘hops’).”
  • In Lesson 9-9, Focus: Measuring in Seconds, “Ask children if they know the name of a unit that the stopwatch can measure. Introduce the word second by explaining that it is the unit of time used by people around the world; explain that a second means the same length of time no matter where you live or what tool you use to measure it, so using seconds allows us to measure time in a way that everyone understands. (Remind them of Lesson 8-3 and mention that a second is about as long as saying ‘one Mississippi.”) With the class, brainstorm activities that take about one second, such as standing up or snapping your fingers once.”

 

Examples of the materials using mathematical language that is not precise or appropriate for the grade level include:

 

  • In Lesson 8-12, Focus: Using Function Machine, “Show and explain the function machine you created. Highlight the in, out, and rule features of the machine. Explain that when a number goes in the machine, something happens to it, and a new number comes out of the machine. The rule tells what will happen to each in number in the machine.”
  • In Lesson 9-2, Practice: Reviewing Function Machines, “Use your function machine box to review how to apply a given rule, such as ‘subtract 2’ or ‘-2’.” Students work in “My First Math Book” p.25. The materials state, “Each child thinks of a rule and writes it in the function machine in his or her own book. Each child also fills in the in numbers. Children then trade books with a partner. Partner much write out the numbers.”
  • In Lesson 9-3, Focus: Playing “What’s My Rule?”, “Show children the function machine box from lesson 8-12 and display an In and Out Chart (Math Masters, page TA64). Point out that the rule is missing from the front of the box. Explain that children will use in and out numbers to figure out the rule.”

Gateway Three

Usability

Not Rated

+
-
Gateway Three Details
This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

Indicator 3a

The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
N/A

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
N/A

Indicator 3c

There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
N/A

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
N/A

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
N/A

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
N/A

Indicator 3g

Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
N/A

Indicator 3h

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
N/A

Indicator 3i

Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
N/A

Indicator 3j

Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
N/A

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
N/A

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
N/A

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
N/A

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
N/A

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
N/A

Indicator 3p

Materials offer ongoing formative and summative assessments:
N/A

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
N/A

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
N/A

Indicator 3q

Materials encourage students to monitor their own progress.
N/A

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
N/A

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
N/A

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
N/A

Indicator 3u

Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
N/A

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
N/A

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
N/A

Indicator 3x

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

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
N/A

Criterion 3z - 3ad

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
N/A

Indicator 3aa

Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
N/A

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
N/A

Indicator 3ac

Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
N/A

Indicator 3ad

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
N/A
abc123

Additional Publication Details

Report Published Date: 10/29/2020

Report Edition: 2020

Title ISBN Edition Publisher Year
Everyday Math 4 Quick Look Activity Pack 9780076718641 McGraw-Hill 2019
Everyday Math 4 Classroom Resource Package 9780077040192 McGraw-Hill 2019
Everyday Math 4 Implementation Guide 9780079049391 McGraw-Hill 2019

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Please note: Reports published after 2021 will be using version 2 of our review tools. Learn more.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

The EdReports rubric supports a sequential review process through three gateways. These gateways reflect the importance of alignment to college and career ready standards and considers other attributes of high-quality curriculum, such as usability and design, as recommended by educators.

Materials must meet or partially meet expectations for the first set of indicators (gateway 1) to move to the other gateways. 

Gateways 1 and 2 focus on questions of alignment to the standards. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?

Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. 

In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Alignment and usability ratings are assigned based on how materials score on a series of criteria and indicators with reviewers providing supporting evidence to determine and substantiate each point awarded.

For ELA and math, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to college- and career-ready standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For science, alignment ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for alignment to the Next Generation Science Standards, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.

For all content areas, usability ratings represent the degree to which materials meet expectations, partially meet expectations, or do not meet expectations for effective practices (as outlined in the evaluation tool) for use and design, teacher planning and learning, assessment, differentiated instruction, and effective technology use.

Math K-8

Math High School

ELA K-2

ELA 3-5

ELA 6-8


ELA High School

Science Middle School

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