Kindergarten - Gateway 1

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Summative assessments include Beginning-of-Year, Mid-Year, and End-of-Year Assessments.

Materials assess grade-level standards. Examples include:

• 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)

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials engage all students in extensive work with grade-level problems. Each lesson provides opportunities during Warm Up, Focus Activities, and Practice. Examples include:

• Lesson 1-6, Count and Sit, Focus: Playing Count and Sit, students' choral count from 0 to 10, “Have the mascot point to one child at a time to prompt each to say the next number. For example, the first child should say ‘1’, the next child should say ‘2’, and so on.” Lesson 4-5, Focus: Taking Ten-Frame Quick Looks, students are flashed ten frames containing different amounts of dots and are asked to remember what they saw after 3 seconds of looking at the ten-frame configuration. “Flash each image for about three seconds before removing (or covering) it and ask children to remember what they saw. To elicit flexible ways of thinking about each image, ask: What did you see? How did you see it?” Lesson 7-3, students are given a “secret” number, and count out the same amount of counters to put in a bag, “Give each child a stick-on note with a ‘secret’ number between 10 and 19 and a resealable plastic bag. Have children count out that number of small objects to put in their bags.” Students engage in extensive work with grade-level problems for K.CC.5, “Count to answer ‘how many?’ questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.”

• Lesson 1-9, Number Stories, Focus: Representing 5, students show different ways to make five fingers using 2 hands. Lesson 4-5, students look at 10 frames filled with different dot combinations and describe how they saw the dots, “I saw 2 and 1, which makes 3.” Lesson 7-12, Dice Addition, students roll 2 dice and add them together, “Give each player a ten frame and a pair of Dice Addition dice. Players roll their dice and announce the resulting addition equation (for example, 2+3=5).” Lesson 8-5, Dice Subtraction, students roll 2 dice and subtract them, “Give each player a blank ten frame and a pair of Dice Subtraction Dice. Players roll their dice and subtract the smaller number from the larger number. Then they state the subtraction equation and tell the difference (4 minus 2 equals 2, for example).” Lesson 9-6, “Roll and Record with Numeral Dice”, students roll 2 dot dice and find the total, “Give each pair of children two 1-6 numeral dice and explain that today they will play with these dice. Have them roll their dice and find the total. Ask: How did you find the total?” These games are also revisited in other lessons during the practice portion of the lesson. Students engage in extensive work with grade-level problems for K.OA.5, “Fluently add and subtract within 5.”

• Lesson 3-5, Longer or Shorter?, Focus: Sorting by Longer and Shorter, students compare strips of paper using the words “longer” and “shorter” “Use strips of different lengths to show and explain the terms longer, shorter, and same length. Hold up pairs of strips and have children compare the strips and describe the relationships.” Lesson 4-9, students are introduced to a pan balance, and use the words “heavier” and “lighter” to describe objects placed in their outstretched hands. “Hold up the two containers you prepared with objects of different weights. Pass them around for children to compare. Ask: How are they the same? Different? Which feels heavier? Lighter? Emphasize that although the containers are the same size, when filled they are different weights: one is heavier; one is lighter. Have a child illustrate the comparison by holding each container in an outstretched arm like a human pan balance.” Lesson 9-5, students measure and weigh backpacks and compare how heavy or light each one is compared to another. “Show children the books they will use to fill the backpacks. Point out that all the books are about the same size, so they can make fair comparisons. Empty the backpacks of any contents and have children fill them with books. Together count the number of books in each backpack. Ask and discuss: Which backpack holds more books (has greater capacity)? Who do you know? With the books inside, which backpack do you think will weigh more? Why?” Students engage in extensive work with grade-level problems for K.MD.2, “Directly compare two objects with a measurable attribute in common, to see which object has "more of"/"less of" the attribute, and describe the difference. For example, directly compare the heights of two children and describe one child as taller/shorter.”

The materials provide opportunities for all students to engage with the full intent of Kindergarten standards through a consistent lesson structure. According to the Teacher’s Lesson Guide, Problem-based Instruction “Everyday Mathematics builds problem-solving into every lesson. Problem-solving is in everything they do. Warm-up Activity- Lessons begin with a quick, scaffolded Mental Math and Fluency exercise. Daily Routines - Reinforce and apply concepts and skills with daily activities. Math Message - Engage in high cognitive demand problem-solving activities that encourage productive struggle. Focus Activities - Introduce new content with group problem-solving activities and classroom discussion. Summarize - Discuss and make connections to themes of the focus activity. Practice Activities - Lessons end with a spiraled review of content from past lessons.” Examples of full intent include:

• Lesson 1-1, Partner Match, Focus: Playing Count and Sit, students play a game to practice the counting sequence. “Explain that for today’s game, your starting number is 1 and your target number is 10. Begin counting with 1 and go around the circle with each child saying the next number in the sequence.” Lesson 4-6, Focus: Counting and Moving With Teens, students are introduced to teen numbers and extend the counting sequence to 19, “Count from 1 to 10 together. Ask: What number comes after 10? Show the portion of your Growing Number Line spanning the numbers 10 through 19 and introduce these as the teen numbers…Count these numbers together as you point to them…” Lesson 5-12, students use a number-grid poster to count by 1s, then by 10s to 100, “Review the Number-Grid Poster by counting by 1s and then by 10s to 100, while you or a child point to the numbers.” Students engage in the full intent of K.CC.1, “Count to 100 by ones and by tens.”

• Lesson 2-5, Pocket Problems, Focus: Solving Pocket Problems, students use counters and a “pocket” to create addition and subtraction problems within 5, “Use five or fewer counters as your starting number and only add or take away one or two counters at first. Each time, have children use their counters to show how many are in the pocket after counters are added or taken away.” Lesson 2-12, students act out number stories within 5, “This morning some squirrels were playing in my yard. 4 squirrels were in a tree and 2 were burying acorns. How many squirrels were there in all? (Parts-and-total problem) Invite children to act out each story or to use counters, fingers, or drawing to model the story as you tell it.” Lesson 5-10, Focus: Using the Addition Symbol, introduces students to the addition symbol drawn on a craft stick. “Give each child 1 craft stick, about 10 counters, and a sheet of construction paper or a slate as a work surface. Show children how to put the craft stick vertically in the middle of their paper or slate. Tell one of the number stories you created and have children model it with counters.” Lesson 6-8, Focus: Using the Subtraction Symbol, students are introduced to the subtractions symbol drawn on a craft stick. “Give each child a craft stick, a sheet of construction paper or a slate as a work surface, and about 10 counters. Tell a ‘take-away’...number story and guide children in modeling the story with counters. Students engage in the full intent of K.OA.1, “Represent addition and subtraction with objects, fingers, mental images, drawings, sounds.”

• Lesson 6-4, Solid-Shapes Museum, Focus: Creating a Solid-Shapes Museum, students are introduced to solid figures, and pass them around to each other while describing what they see and feel. “Hold up a cylindrical object, such as a soup can. Say: The shape of this ____ is similar to a cylinder. Ask children to describe the cylinder in many ways. Lesson 6-5, Focus: Comparing Flat and Solid Shapes, students are introduced to the terms 2-dimensional and 3-dimensional shapes and describe the differences. Students then use solid shapes to “stamp” the faces on paper to create flat shapes. “ In a small group, have children stamp different faces of various solid shapes onto paper. Ask questions to encourage them to make predictions before stamping.” Lesson 7-4, Playing Solid-Shapes Match Up, students describe shapes as 2- or 3- dimensional, “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.” Students engage in the full intent of K.G.3, “Identify shapes as two-dimensional (lying in a plane, "flat") or three-dimensional ("solid").”

Materials do not provide opportunities for all students to engage with the full intent or extensive work with K.NBT.1, “Compose and decompose numbers from 11 to 19 into ten ones and some further ones.” Examples include:

• K.NBT.1 is addressed in 5 lessons: Lesson 5-6 Focus (20-30 minutes), Lesson 5-8 Focus (20-30 minutes), Lesson 7-3 Focus (20-30 minutes), Lesson 8-6, Focus (20-30 minutes), and Lesson 8-13 Focus (20-30 minutes). Five opportunities over the course of a school year do not provide opportunities for extensive work with K.NBT.1. 

• K.NBT.1 is addressed in “Number of the Day” Routine 1, students track the number of the day on a growing number line and represent the number with objects. This activity is done as a class and does not provide individual opportunities for students to engage in the full intent of a major learning standard of the grade.

The materials reviewed for Everyday Mathematics 4 Kindergarten meet expectations that, when implemented as designed, the majority of the materials address the major work of each 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 does not include explicit instructions. Therefore, it cannot be determined if all students would be working on major work of the grade.

A lesson analysis is most representative of the materials. As a result, approximately 71% of the materials focus on the major work of the grade.

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

Digital materials’ Main Menu links to the “Spiral Tracker” which provides a view of how the standards spiral throughout the curriculum. The Lesson Landing Page contains a Standards section noting standards covered by the lesson. Teacher Edition contains “Correlation to the Standards for Mathematics” listing all grade-level standards and correlating lessons. Examples include:

• Lesson 1-2, Introduction to Pattern Blocks, 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 four 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.”

• Lesson 2-7, Day 2-Introduction to Sorting, Focus: Solving the Open Response Problem, students sort a collection of items according to attributes into different categories and then count the items, “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 the same about the objects in this group? What is different between this group and that group of objects? What is your rule for sorting your objects? How many objects are in each group? Which has the most? The fewest?” 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.”

• Lesson 3-1, Pattern-Block Graph, Focus: Graphing Pattern Blocks, students sort pattern blocks into different categories and then compare the categories by answering questions involving fewer and greater, “Place a handful of pattern blocks where children can see them. Have children share ways they could sort the blocks. If no one mentions it, suggest sorting the blocks by shape and invite children to help you do this. Ask: How can we find out which shape has the most? the least (fewest)?” 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.”

• Lesson 4-1, Attribute Blocks, 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, “Sort the blocks by color as children watch. Then have the children explain why each group of blocks belongs together. Ask: How did I sort the blocks? What was my sorting rule? Why do these blocks belong together? How are they alike? How are they different? How many blocks are in each group? Are there more red blocks or blue blocks?” 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.”

• Lesson 9-4, Backpack Math: Height, Width, and Area, Focus: Measuring and Comparing Backpacks, students compare the heights of two different backpacks using connecting cubes to measure, “Have children use connecting cubes to measure the heights and widths of their backpacks, record their findings (and their partner’s) on their My First Math Book pages, and compare the measurements. As children work, circulate and ask: How tall (or wide) is your backpack? Your partner's? Which backpack is taller (or wider).” 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.”

The materials reviewed for Everyday Mathematics 4 Kindergarten 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.

The Teacher Edition contains a Focus section in each Section Organizer identifying major and supporting clusters covered. There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:

• Lesson 1-8, Class Age Graph, Focus: Making an Age Graph, students practice counting the number of students in different age groups and then discuss which line has more or less people, “Compare the number of children in different age groups. Ask: Which age has more (the most) children? How many more 5-year olds are there than 6-year olds?” This connects the major work of K.CC.A, “Know number names and the count sequence” to the major work of K.CC.C, “Compare numbers.” 

• Lesson 2-3, Getting to Know Triangles, Focus: Getting to Know Triangles, students identify and describe triangles using their attributes, then find or draw pictures of triangles to create a collage, “Conclude by inviting children to create a class triangle collage or several group collages. Have them cut triangles from magazines and glue them to the posterboard triangle or draw them on directly.” This connects the supporting work of K.G.A, “Identify and describe shapes” to the supporting work of K.G.B, “Analyze, compare, create, and compose shapes.”

• Lesson 2-12, Number Stories, Practice: Revisiting Shape Collages, students sort shape cards onto the proper collage and describe their sorting attributes, “With the class, sort the triangle, rectangle, and circle Shape Cards onto the proper collage and review what each shape family has in common. Look at the remaining Shape Cards and prompt children to identify ways they might group some of them (curved shapes, for example).” This connects the supporting work of K.G.A, “Identify and describe shapes” to the supporting work of K.G.B, “Analyze, compare, create, and compose shapes.”

• Lesson 4-12, Top-It With Number Cards, Focus: Playing Top-It with Number Cards, students pick two number cards from a deck to compare, “Pick two cards from the deck. Have children say the numbers and tell you which number is greater (more, higher) and which number is less (fewer, lower). Ask: How do you know which number is greater?” This connecte the major work of K.CC.A, “Know number names and the count sequence,” to the major work of K.CC.C, “Compare numbers.”

• Lesson 5-8, Teens on Double Ten Frames, 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, “In pairs, have children take turns spinning a number and placing that number of counters on their double ten frame using the ‘10 and some more’ approach (filling one ten frame first). After each child has a turn, they compare their double ten frames. The child with the largest number wins the round. (Vary the game by having the smallest number win the round).” This connects the major work of K.CC.C, “Compare numbers” to the major work of K.NBT.A, “Work with numbers 11-19 to gain foundations for place value.” 

• Lesson 6-9, Disappearing Train, 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, “For example, if you have 9 train cars and roll 2, say ‘I had 9 train cars. I rolled ‘minus 2,’ so I take 2 cubes from my train. How many cars do I have now? How do you know?’” This connects the major work of K.CC.B, “Count to tell the number of objects” to the major work of K.OA.A, “Understand addition as putting together and adding to, and understand subtraction as taking apart and taking from.”

• Lesson 8-2, Marshmallow and Toothpick Shapes, Focus: Modeling Shapes, students create 2-D and 3-D shapes with toothpicks and marshmallows, “Promote exploration, description, and discovery with prompts such as: How did you make the window? What shapes did you use? How do you make a pyramid? How many marshmallows and toothpicks do you need? Can you make a shape with sides that are different lengths? How could you attach those triangles to each other? What shape will you make if you attach those two cubes?” This connects the supporting work of K.G.B, “Analyze, compare, create, and compose shapes” to the supporting work of K.MD.A, “Describe and compare measurable attributes.”

The materials reviewed for Everyday Mathematics 4 Kindergarten 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.

Materials relate grade-level concepts to prior knowledge from earlier grades. Each Section Organizer contains a Coherence section with “Links to the Past” containing information about how focus standards developed in prior units and grades. 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 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 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.” 

Materials relate grade-level concepts to future work. Each Section Organizer contains a Coherence section with “Links to the Future” containing information about how focus standards lay the foundation for future lessons. Examples include:

• 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 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.”

Materials contain content from future grades in some lessons that is not clearly identified. Examples include:

• Lesson 1-13, Shape Patterns, Focus: Patterning with Shapes, students use shapes to build patterns, “Build from children’s responses to explain that a pattern repeats or grows. Explain that they just saw two different kinds of patterns: a repeating pattern and a growing pattern. After the last pattern, have children turn to a partner and complete the sentence frame: I know this is a pattern because_______.”  This lesson is labeled K.G.1, “Describe objects in the environment using names of shapes, and describe the relative positions of these objects using terms such as above, below, beside, in front of, behind, and next to” and K.G.2, “Correctly name shapes regardless of their orientations or overall size." Identifying patterns is a grade standard, 4.OA.5, “Generate a number or shape patterns that follow a given rule."

• Lesson 4-3, Favorite Color Graphs, Focus: Graphing Favorite Colors, “Model how to label the axes on the graph with the color names and the 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…”)

• Lesson 5-6, Teen Patterns, Practice: Solving Number Stories, students solve problems in their journals, “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."