1st Grade - Gateway 1

The materials reviewed for Everyday Mathematics 4, Grade 1 meet expectations for assessing grade-level content, and if applicable, content from earlier grades.

Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year. Unit Assessments found at the end of each unit assess the standards of focus for the unit. Open Response Assessments found at the end of odd-numbered units provide tasks addressing one or more content standards. Cumulative Assessments found at the end of even-numbered units include items addressing standards from prior units.

Materials assess grade-level standards. Examples include:

• Unit 3 Open Response Assessment, Item 1, “Use the number line to help you solve the story. You are collecting leaves. You have 3 leaves in your pocket. You pick up some more leaves. Now you have 10 leaves. How many leaves did you pick up?” (1.OA.1)

• Unit 4 Assessment, Item 6, “Ali has 7 red crayons, 3 yellow crayons, and 7 blue crayons. How many crayons does he have in all? Explain how you found the sum.” (1.OA.2)

• Unit 6 Cumulative Assessment, Item 2, “Alice says that if she knows that 8+9=17, then she also knows that 9+8=17. Is Alice correct? Explain why or why not.” (1.OA.3)

• Mid-Year Assessment, Item 13, “Shelby and James used paper clips to measure a marker. Shelby measured like this: James measured like this: Who measured correctly? Tell why you think so.” (1.MD.2)

Materials assess above-grade assessment items that could be removed or modified without impacting the structure or intent of the materials. Examples include:

• Unit 3 Assessment, Item 7, “Fill in the rule and the frames.” (4.OA.5)

• Unit 7 Assessment, Item 11, “Find the rule. Fill in the missing numbers.” Students look at a function table containing in and out boxes, determine the rule, and fill in the missing numbers. (4.OA.5)

• End-the-Year Assessment, Item 5, “Fill in the rule and the missing numbers.” Students find the pattern, subtract 10, and fill in the missing numbers and rule when shown 95, 85, 75, ___, ___, 45, 35. (4.OA.5)

The materials reviewed for Everyday Mathematics 4 Grade 1 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 1-2, Investigating the Number Line, Focus: Introducing Monster Squeeze, students identify numbers that fall between a set of numbers, “The leader thinks of a mystery number and then calls out two numbers such that the mystery number is somewhere between them. The other children try to guess the mystery number.” Students also play “Monster Squeeze in Lesson 1-6, Practice. Lesson 5-1, students are introduced to “The Digit Game” to compare 2-digit numbers, “Have children play The Digit Game to practice comparing 2-digit numbers using place value. Before partners play, demonstrate a round or two. Ask children to make arguments for why one number is larger than the other based on the number of tens or ones each digit represents. Lesson 5-4, Core Activities, Focus: Introducing Relation Symbols > and <, students are introduced to comparison symbols and write the symbols to create comparison statements, “Dictate pairs of numbers, such as 13 and 12, 11 and 20, 24 and 42. Have children write the numbers on their slates and write the correct relation symbol between them.” Lesson 6-8, Math Masters, Problem 4, students use symbols to complete comparison statements, “Use >, <, or = to make each number sentence true.” Students engage in extensive work with grade-level problems for 1.NBT.3, “Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.”

• Lesson 4-10, Core Activities, Focus: Adding Three Numbers, students solve word problems independently, “Tell the following number story: Our class has 7 pencils, 4 pens, and 3 crayons. How many writing tools do we have in all? Ask children to independently solve the problem. Then discuss their strategies. Write number models and discuss different ways to find the sum.” Lesson 5-3, Warm Up: Mental Math And Fluency, students solve a number story with 3 addends, “Sheena read 7 books in April, 6 books in May, and 4 books in June. How many books did Sheena read in all?” Lesson 5-9, Home Link, Math Masters, students solve a word problem with 3 addends, “Sandra’s cat had 3 gray kittens, 2 spotted kittens, and 4 white kittens. How many kittens did she have in all? ___ kittens  Number model: ___ + ___ + ___ = ___.” Students engage in extensive work with grade-level problems for 1.OA.2, “Solve word problems that call for the addition of three whole numbers whose sum is less than or equal to 20.”

• Lesson 6-1, Adding Three Numbers, Focus: Reading Hour-Hand-Only Clocks, students are introduced to the “hour” and how long an hour is, “Use the demonstration clock made from Math Masters, page 156. Starting at 12 o’clock, move the hour hand clockwise and have children call out the hours as the hour hand passes through one hour to the next.” Lesson 9-2, Practice: Home Link, students practice writing hands on a clock to reflect the time. Problem 2, “Record the time.” Lesson 9-7, Math Journal 2, p. 205, Problem 5, students are shown an analog and digital clock, both reading 5:30. “Do these clocks show the same time? Explain how you know.” Routine 6, Math Any Time Routine: Daily Schedule, “Later in the year, use the daily schedule to reinforce clock reading skills. Have children show certain times on clocks from Math Masters, page R6, and place them next to the appropriate activity, or set toolkit clocks to the time of each activity. Initiate questions about these events throughout the day.” Students engage in extensive work with grade-level problems for 1.MD.3, “Tell and write time in hours and half-hours using analog and digital clocks.”

The materials provide opportunities for all students to engage with the full intent of Grade 1 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 2-9, Change-to-Less Number Stories, Focus: Solving Mystery Cup Problems, students use subtraction to solve, “Imagine there are 10 cups. I knock some over. There are 7 cups left standing. How many cups did I knock over?” Students share their strategies, which may include, “What do I need to add to 7 in order to get 10? To emphasize the…strategy, provide another example and ask children to think addition to figure out how many cups were knocked over.” Lesson 5-10, Core Activities: Focus, Introducing The Difference Game, students play a game comparing quantities of pennies, “Think aloud: How many more do I need to add to (the smaller set) to make it equal to (the larger set)? Help children see that thinking of the missing addend will help them find the difference.” Students engage in the full intent of 1.OA.4, “Understand subtraction as an unknown-addend problem.”

• Lesson 4-11, Core Activities: Finding “Ten Friends”, students explore a number grid and identify 26, 36, and 46, “Ask: What column are these numbers in? What do you notice about all the numbers in this column? What else do you notice about 26, 36, and 46? Tell children that 26, 36, and 46 are part of a number-grid column family. We can think of these column families as sharing the same ‘last name’...but having different ‘first names’.” Students identify 10 more than 36 and 10 less than 36 and continue practicing with different numbers posed by the teacher. Lesson 8-10, Core Activities: Focus, Introducing Number Grid Puzzles, students are shown number grid pieces with missing numbers, and students find the missing numbers by adding or subtracting 10 from the number shown, “How could you show the number that is 10 more than 55? 10 less than 55? Explain that moving within a column on the number grid is like adding or subtracting longs.” Students engage in the full intent of 1.NBT.5, “Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count; explain the reasoning used.”

• Lesson 7-6, 10 More, 10 Less, Focus: Exploration B: Dividing Shapes, students use geoboards to create shapes, “Children create shapes on geoboards and then divide them into two parts. Encourage children to find multiple ways to divide the shapes and to use multiple methods to test whether the parts are the same size.” Lesson 8-2, Core Activities, Focus, Naming Shares, the teacher creates a “Two Equal Shares” poster with the students. The poster includes “half, 1 half, 1 out of 2 parts” for the name of one share, and “whole, 2 halves, 2 out of 2 parts” for the name of all shares, “Encourage children to find multiple ways to divide shapes to use multiple methods to test whether the parts are the same size.” Lesson 8-4, Math Masters, students partition shapes to solve, “Two girls share one paper square. Four boys share the same-size square of paper. Tell who will get a larger share of paper, one girl or one boy. Make a drawing of the problem. Explain your answer.” Students engage in the full intent of 1.G.3, “Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters and use the phrases half of, fourth of, and a quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.”

Materials do not provide opportunities for all students to engage with extensive work with the full intent of 1.NBT.1, “Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.” Examples include:

• 1.NBT.1 is addressed in the Focus section of several lessons throughout Units 1-5 and embedded in Daily Routines which explore and extend the real-world application of math. However, only two of these lessons, Lesson 1-11 and Lesson 3-8, meet the full intent of 1.NBT.1 by involving number charts to 120. Two opportunities over the course of a school year do not provide extensive work with the full intent of 1.NBT.1. 

• Examples provided to teachers are within 100 and should extend the counting sequence to 120 as the standard states. For example, in Lesson 1-11, Focus: Introducing the number grid, the materials provide a total of 12 examples for students to practice counting up and counting back by 1s and 10s. All 12 examples are within 80, “Start at 26 and count back 4 hops. Where do you land?” or “Start at 70 and count back 10 hops. Where do you land?”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations that, when implemented as designed, the majority of the materials address the major work of each grade.

• There are 9 instructional units, of which 6 units address major work of the grade or supporting work connected to major work of the grade, approximately 67%.

• There are 109 lessons, of which 72.5 address major work of the grade or supporting work connected to the major work of the grade, approximately 67%.

• In total, there are 170 days of instruction (109 lessons, 37 flex days, and 24 days for assessment), of which 101 days address major work of the grade or supporting work connected to the major work of the grade, approximately 59%. 

• Within the 37 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.

A lesson analysis is most representative of the materials. As a result, approximately 67% of the materials focus on the major work of the grade.

The materials reviewed for Everyday Mathematics 4 Grade 1 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 1-1, Focus: Introducing First Grade Everyday Mathematics, students discuss items around the room. “Have children find and name numbers and shapes in the classroom. Encourage them to explain how they might use numbers and to describe the features of the shapes. For example, children may notice that they can use numbers on the clock to tell time or that the door to the classroom is a rectangle with four sides.” This connects supporting standard 1.G.1, “Distinguish between defining attributes versus non-defining attributes,” to the major work of 1.NBT.1, “Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.” 

• Lesson 1-8, More Organizing Data, Focus: Organizing and Representing Data in a Tally Chart, students select a data collection topic, create a tally chart, and answer questions about data in the tally chart. “Ask children what they can learn from the tally chart. Ask specifically about the total number of data points in each category and how many more or less there are in one category than another.” This connects the supporting standard 1.MD.4, “Organize, represent, and interpret data with up to three categories,” to the major work of 1.OA.6, “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.”

• Lesson 4-6, Representing Data with a Bar Graph, Focus: Building a Superhero Bar Graph, students make a tally chart of what superhero power classmates would choose (to fly, be invisible, or have extra strength). Students then make a bar graph of the same data and answer questions comparing the data. “Ask questions about the super power data children collected and have them record their answers on slates. Ask how many children chose each of the super powers. Then pose questions that require children to combine and compare the data from two of the categories.” This connects the supporting standard 1.MD.4, “Organize, represent, and interpret data with up to three categories,” to the major work of 1.OA 6, “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.”

• Lesson 7-11, Digital Clocks, Focus: Introducing the Minute Hand, students discuss the length of a minute and an hour while identifying the minute and second hand on an analog clock. Students clap in unison and count up to 60 to know the length of a minute. “After children share their ideas about the length of a minute, ask them how they could check whether their lists make sense. If no one mentions it, tell children there are 60 seconds in a minute so they can count each second from 1 to 60 to estimate the length of one minute. Help children estimate one minute by counting and then clapping in unison: 1 (clap), 2, (clap), 3, (clap), and so on, to 60, (clap).” This connects the supporting standard 1.MD.3, “Tell and write time in hours and half-hours using analog and digital clocks,” to the major work of 1.NBT.1, “Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral.”

• Lesson 8-6, Dimensional Shapes, Practice: Making a Shapes Bar Graph, students practice building composite shapes with square, triangle, and trapezoid pattern blocks. Students then record the number of shapes they used on a bar graph and work with a partner to ask questions about the graphs. “Ask them to record how many of each shape they used in the bar graph on journal page 171. Then have them work in partnerships to ask questions about the graphs. Model a few sample questions such as: How many more squares than trapezoids did you use? How many blocks did you use altogether?” This connects the supporting work of 1.G.2, “Compose two-dimensional shapes or three-dimensional shapes to create a composite shape,” to the major work of 1.OA.1, “Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations for including problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The Teacher Edition contains a Focus section in each Section Organizer identifying major and supporting clusters covered. Materials do not contain connections from supporting work to supporting work. There are connections from work and major work to major work throughout the grade-level materials, when appropriate. Examples include:

• Lesson 1-5, 1 More, 1 Less, Focus: Bunny Hop, while playing a game, students use a number line to count up and back, “Ask children how they knew what numbers they needed to reach the hole (or carrot). Reinforce their answers with statements such as, ’Maria saw that she needed 3 hops to get from 7 to 10, so she hoped that she would roll a 3. She knew that 10 is 3 more than 7.’” This connects the major work of 1.OA.C, “Add and subtract within 20 connects” to the major work of 1.NBT.A, “Extend the counting sequence.”

• Lesson 2-10, Number Models, Focus: Introducing Addition Number Models, students use plus and equal signs to write number models for change-to-more word problems, “Do another penny drop with a change-to-more diagram. Encourage children to use the Strategy Wall to find the sum. Then ask children to record number models on their slates. Have them share their number models with the class.” This connects the major work of 1.OA.A, “Represent and solve problems involving addition and subtraction” to the major work of 1.OA.C, “Add and subtract within 20.”

• Lesson 5-11, Two-Digit Addition and Subtraction, Focus: Subtracting Animal Weights, students use a variety of strategies to find the difference in weights of pairs of animals, “Pose the following problem. Allow children to share answers and ideas for solving it. Discuss the tools and strategies listed below. Work with children to summarize the problem with a comparison diagram and a couple of number models. How much more does a boy (50lb) weigh than an octopus (20lb)?” Subtracting tens and Counting up to subtract are explained.” This connects the major work of 1.NBT.B, “Understand place value” to the major work of 1.NBT.C, “Use place value understanding and properties of operations to add and subtract.”

• Lesson 8-8, Time to the Half Hour, Focus: Introducing Time to the Half Hour, students shade a clock face and determine how much time this represents. “Compare the different representations and discuss how both pieces of the clock must be equal to be divided in half. Ask, What would you name the part of the clock that you shaded? Tell children that today they will use what they know about halves to learn more about telling time.” This connects the supporting work of 1.MD.B, “Tell and write time” and 1.G.A, “Reason with shapes and their attributes.” 

• Lesson 9-1, Review: Measurement, Focus: Measuring with Rulers, students measure objects with paper “rulers”, which are pieces of paper with a paperclip drawing that students previously cut out and pasted together. Students, “explain their strategies for determining the total number of paper clips when the ruler is moved several times. For example: Maria said that the bulletin board is 3 rulers plus 7 more paper clips wide. How many paper clips are in 1 ruler? 10 How do you find the number of paper clips in 3 whole rulers? Sample answer: Count by 10s: 10, 20, 30. What should you do to find the total width of the bulletin board? Add 7 paper clips to 30; 37 paper clips in all.” This connects the major work of 1.MD.A, “Measure lengths indirectly and by iterating length units” to the major work of 1.NBT.C “Use place value understanding and properties of operations to add and subtract.”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

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 1.NBT.1, “In Kindergarten, children learned to count to 100 by 1s and by 10s.”

• Teacher’s Lesson Guide, Section 5 Organizer, Coherence, “Links to the Past” for 1.NBT.4, “In Kindergarten, children developed an understanding of teen numbers as 10 ones and some further ones.”

• Teacher’s Lesson Guide, Section 8 Organizer, Coherence, “Links to the Past” for 1.G.2, “In Unit 7, children explored 2-dimensional shapes with different attributes, reviewing various common shapes such as triangles and rectangles. In Kindergarten, children composed small shapes to form larger shapes.”

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 1 Organizer, Coherence, “Links to the Future” for 1.OA.5, “In Unit 3, children will utilize number lines to keep track of counts as they solve addition and subtraction problems. In Grade 2, children will use their understanding of the relationship between addition and counting to make sense of the properties of even and odd numbers.”

• Teacher’s Lesson Guide, Section 3 Organizer, Coherence, “Links to the Future” for 1.NBT.1, “In Unit 5, children will use the patterns they observed when counting within 100 to expand the number grid to larger numbers as they create number scrolls. In Grade 2, children will extend this even further as they count and represent numbers to 1000.”

• Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Future” for 1.NBT.4, “In Unit 9, children will revisit adding and subtracting within 100. In Grade 2, children will extend their strategies to solve addition and subtraction problems within 1000, with a focus on developing fluency within 100.”

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

• Lesson 3-5, Counting on the Number Line, Focus: Reviewing Skip Counting on Number Lines, “When children have completed the journal page, encourage them to discuss and compare any patterns they see in the different skip-counts. Ask: Why does it take more hops to count to 20 by 5s than it does by 10s?” This lesson is labeled 1.NBT.1, “Counting to 120, starting at any number less than 120." Counting by 5s and 10s is 2.NBT.2, “Count within 1,000; skip-count by 5s, 10s, and 100s."

• Lesson 7-8, Finding Unknowns: “What’s My Rule?”, Focus, Finding Unknowns: What’s My Rule?, “Display a function machine. Explain that the function machine is like the magic bag. If you put a number into the machine, the number will follow the rule on the machine, and a different number will come out. Any number you put in will follow the same rule. Tell children that if you put 3 in this machine, 4 will come out. If you put in 6, 7 will come out...Ask: What number do you think will come out if you put in 5?” This lesson is labeled 1.OA.6, “Add and subtract within 20." Function tables is 4.OA.5, “Generate a number or shape pattern that follows a given rule."