1st Grade - Gateway 1

The materials reviewed for Eureka Math² Grade 1 meet expectations for assessing grade-level content and, if applicable, content from earlier grades. 

The curriculum is divided into six modules and each includes a Module Assessment. Examples of grade-level items from Module Assessments include:

• Module 1, Module Assessment, Item 6, students see a partially filled ten-frame with four dots on top and four dots underneath. “Write a doubles number sentence.” (1.OA.7)

• Module 3, Module Assessment, Item 4, students see base ten blocks showing two tens and six ones and an empty number bond with ___ tens ___ ones underneath. “Write as tens and ones.” (1.NBT.2)

• Module 4, Module Assessment, Item 1, students see two pictures, one with a girl by a bench and the other with a dog sitting by a bench. “1. Circle. The dog is taller, shorter than the girl. Draw or write to order the bench, girl, and dog from shortest to tallest.” (1.MD.1)

• Module 6, Module Assessment, Part 1, Item 1, “Read: There are 2 small cakes. Cut 1 cake into halves. Cut 1 cake into fourths. Draw: Color 1 half. Color 1 fourth. Write: Which piece is larger? Circle. 1 half of the cake, 1 fourth of the cake, Why?” (1.G.3)

The materials reviewed for Eureka Math² Grade 1 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. 

According to the Grade 1 Implementation Guide, “Each lesson is structured in four sections: Fluency, Launch, Learn, and Land. Lessons are designed for one 60-minute instructional period. Fluency provides distributed practice with previously learned material. It is designed to prepare students for new learning by activating prior knowledge and bridging small learning gaps. Launch creates an accessible entry point to the day’s learning through activities that build context and often create productive struggle that leads to a need for the learning that follows. Every Launch ends with a transition statement that sets the goal for the day’s learning. Learn presents new learning related to the lesson objective, usually through a series of instructional segments. This lesson component takes most of the instructional time. Suggested facilitation styles vary and may include direct instruction, guided instruction, group work, partner activities, interactive video, and digital elements. The Problem Set, an opportunity for independent practice, is included in Learn. Land helps you facilitate a brief discussion to close the lesson and provides students with an opportunity to complete the Exit Ticket. In the Debrief portion of Land, suggested questions, including key questions related to the objective, help students synthesize the day’s learning. The Exit Ticket provides a window into what students understand so that you can make instructional decisions.”

Instructional materials engage all students in extensive work with grade-level problems through the consistent lesson structure. Examples include:

• Module 1, Lesson 3 and Module 2, Lesson 23 engage students in extensive work with 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another). Module 1, Lesson 3: Sort to represent and compare data with three categories, Learn, students generate data by sorting and counting, and then represent the data on a graph. “Partner students and distribute a bag of cubes to each pair. Direct students to sort by color and count each group. Depending on the available workspace, consider having students sort their cubes on a personal whiteboard so they can easily move their cubes as needed. When most pairs are finished, ask students to turn to the My ___ graph and get out crayons and a pencil. Display the incomplete graph to guide the class in graphing their own cube collections. First, invite students to complete the title frame with a word or phrase that tells what they are graphing. Then model graphing the first category. ‘How can we use these number paths to make a graph to show our color groups?’ (We can use one path for each color. We can use our crayons to color how many cubes there are in each group.) ‘How can we label this number path to show the red cubes?’ (We can write the word red or draw a red square next to it.) ‘How can we show how many red cubes we have?’ (We can color the same number of squares as there are red cubes. We can write the total in the box.) Have students use their cubes to complete their graphs independently. Observe and support as needed. When students finish, ask them to put away their cubes. Use the following prompt to have them turn and talk about the graph. ‘What does the graph tell you about the cubes?’ Listen for students to share the totals of each category and comparisons of categories. Some may even find the total of all their cubes.” In the Land section, students sort to represent and compare data with three categories. “Display the Apple Count graph. Facilitate a discussion about what information graphs provide and what we can learn from them.” Module 2, Lesson 23: Compare categories in a graph to figure out how many more, Launch, students create a three-category vertical bar graph with sticky notes and ask questions as a class. “Scatter and display the farm animal counters. Ask students to turn and talk about what they notice. Then ask students to share ideas about how to sort the animals into groups by using attributes such as the following: color, animal type, number of legs, where the animal lives on a farm, actual size of the animal. ‘Let’s group them by different kinds of animals, or animal types.’ Sort the farm animal counters into piles of cows, hens, and pigs. ‘How can we organize our groups to compare them?’ (We could line them up: cows, hens, pigs.) ‘Let’s line them up like a graph. Let’s line up groups carefully so we can see matches. They can go up and down or side to side.’ Organize the groups into columns that follow this order: cows, hens, pigs. Have students count as you place each animal in a line. Use a sticky note to record the total number of animals in each group. Place the total above each column. ‘The lines of animals go up and down instead of side to side. Can we still compare the groups?’ (Yes.) Have students take out their books and turn to the first three-category graph. ‘We can graph our sort by using the number paths and labels on this page. What did we sort?’ (Farm animals) ‘Let’s write that as the title of the graph.’ Help students recall what they know about the parts of a graph from module 1 by asking questions such as the following: How should we use the number paths to show our sort? Why are there pictures of a cow, a hen, and a pig on this graph? Notice the word totals. What belongs in each gray box? Allow time for students to complete the graph by using the class sort. Then transition students to the next segment by framing the work. ‘Today, we will ask and answer questions about the data on this graph.’” 

• Module 1, Lesson 13 and Module 3, Lesson 7 engage students in extensive work with 1.OA.6 (Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten; using the relationship between addition and subtraction; and creating equivalent but easier or known sums.)  Module 1, Lesson 13: Count on from an addend in add to with result unknown situations, Learn, Represent and Solve: Rock Problem, students represent and solve an add to with result unknown problem. “Display the word problem: Hope has 7 rocks. She adds 3 more rocks. How many rocks does she have now? Prompt students to think-pair-share about how to represent and solve the problem. Consider charting their ideas.”  Module 3, Lesson 7: Make ten when the first addend is 8 or 9, Fluency, Whiteboard Exchange: Take Out 2, students use cards to determine what needs to be added to make a group of 10. “After asking each question, wait until most students raise their hands, and then signal for students to respond. ‘Raise your hand when you know the answer to each question. Wait for my signal to say the answer.’ Display the 5-group card that shows 9. ‘How many dots?’ (9) ‘How many more dots to make ten?’ (1) Display the 5-group card filled to 10. ‘When I give the signal, say the addition sentence starting with 9.’ (9+1=10) Display the addition sentence. Repeat the process with the following sequence: (six more problems are included for practice).” In the Launch, students make ten when one number is eight. “Display the picture of a roller coaster. ‘What do you notice?’ (8 children are on the roller coaster. 6 children are waiting in line. The roller coaster is not full. There are two spots open.) ‘What are some ways to figure out how many children there are in all?’ (We could count on from 8. We could fill up the roller coaster and make ten!) ‘Let’s make ten. There are 8 children on the roller coaster. How many more children make ten?’ (2) ‘Where can we get 2 children to fill the roller coaster?’ (2 children from the line can get on the roller coaster. We can break up the 6 children in line into 2 children and 4 children.)” In Land, Exit Ticket, students solve an addition problem using strategies from the lesson and create a new addition sentence for the same problem. “Make 10 to add. Draw how you know. 8+5=___, Write a new number sentence.”

• Module 5, Lessons 6 and 15 engage students in extensive work with 1.NBT.6 (Subtract multiples of 10 in the range 10-90 from multiples of 10 in the range 10-90 [positive or zero differences], using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.) Lesson 6: Add 10 or take 10 from a two-digit number, Launch, students count up and back by tens on a rekenrek. “Show students the rekenrek. Start with all the beads to the right side. ‘Say how many beads there are as I slide them over.’ Slide over 6 beads in the first row all at once. (6) Slide over 10 beads in the second row all at once. (16) ‘How do you know there are 16?’ (6 and 10 is 16.) Continue to slide over 10 beads all at once in each row until 86 beads have been moved. Have students count by tens to 86 as you move each row of beads. Display the ascending tens and ones chart. ‘These are the numbers we counted. The chart shows each number’s digits in the tens place and in the ones place. What do you notice?’ (The digit in the ones place is always 6. The digit in the tens place changes. It goes up 1 each time.) Highlight the digits in the tens place. ‘There is a pattern. We added 1 ten each time. What is the value of 1 ten?’ (10) Write + 10 next to the chart. ‘Suppose we add another ten. What is the new total? How do you know?’ (96. You can use the chart to see the next number. 9 comes after 8. 6 stays the same.) Repeat the process, this time starting with 96 on the rekenrek and counting back by tens. Stop at 16. Display the descending tens and ones chart. Ask students to identify the pattern. Label the chart – 10. Have students use the pattern to figure out the final number, 6.” Lesson 15: Count on and back by tens to add and subtract, Fluency: Beep Counting By 10s, students complete a number sequence counting by tens. “Listen carefully as I count by tens. I will replace one of the numbers with the word beep. I will count up, and I will count down. Raise your hand when you know the beep number. Ready?” Sequences include counting up and back by tens.

The instructional materials provide opportunities for all students to engage with the full intent of all Grade 1 standards through a consistent lesson structure. Examples include:

• Module 1 and fluency activities throughout Modules 4, 5 and 6 engage students 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). Module 1, Lesson 25: Organize, count & record a collection of objects, Learn, Organize, Count, and Record, students use their own strategies to organize and count up to 120 objects and record their process. “Partner students, and invite them to choose a collection, organizing tools (if they would like them), and space to work. Circulate and notice how students organize, count, and record. (See possible student work in the chart below.) Counting strategies may include counting by ones or another familiar number (twos, fives, tens) or counting subgroups and adding them to find the total. Recordings may include drawings, tally charts, numbers, expressions, or number sentences. Use the following questions and prompts to assess and advance student thinking: ‘What is your plan? Show (or tell) me how you are counting. How are you keeping track of what you already counted and what you still need to count? How does what you drew or wrote show how you counted your collection?’ If needed, prompt students to record their collection: ’Can you write or draw something on your paper to show how you counted? Can you write numbers or number sentences to show your collection?’ Select student work that highlights the usefulness of organization in terms of the counting or recording to share in the next segment.” Module 6, Lesson 22: Represent and solve add to and take from with start unknown word problems, Fluency: Happy Counting by Ones from 100-120, students visualize a number line while counting aloud to build fluency counting within 120. “Invite students to participate in Happy Counting. ‘Let’s count by ones. The first number you say is 100. Ready?’ Signal up or down accordingly for each count. Continue counting by ones to 120. Change directions occasionally, emphasizing crossing over 110 and where students hesitate or count inaccurately.”

• Module 5, Lessons 7 and 8 engage students with the full intent of 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 7: Use place value reasoning to compare two quantities, Learn, “‘Which picture shows more marbles?’ (The picture with jars of marbles shows more.) Invite students to think–pair–share about the picture of jars of marbles. ‘How do you know that the picture with jars of marbles shows more marbles?’ Support student-to-student dialogue during discussion by inviting the class to agree or disagree, ask a question, share a new idea, or restate an idea in their own words. (There are 4 jars with 10. We can only make 3 groups of 10 in the other picture. 4 tens is more than 3 tens, so 41 is greater than 39. 41 comes after 39 when we count. 4 tens is 40. 3 tens is 30. So, 41 marbles is more than 39.) ‘41 marbles is more than 39 marbles because 4 tens is more than 3 tens. Does it matter that 39 has 9 ones and 41 only has 1 one? Why?’ (No, because 41 has more tens. Tens are bigger than ones.) Have students write the greater than symbol in the number sentence. ‘We started with 4 tens and 19 ones. When we compose another ten, how many tens and ones are there?’ (5 tens 9 ones) ‘What number is 4 tens and 19 ones?’ (59) ‘What number is 5 tens and 6 ones?’ (56) Tell students to write a symbol between the totals at the bottom of the page to make a true number sentence. Confirm that 59 is greater than 56.” Lesson 8: Use place value reasoning to write and compare 2 two-digit numbers, Land, Debrief, students use place value knowledge to make two-digit numbers, compare the numbers, and make comparison number sentences for the pairs. Students see the digits, 0-9, displayed. “‘These are all the digits. Let’s read them together.’ (0, 1, 2, 3, 4, 5, 6, 7, 8, 9) ‘When we write a digit in the tens place and a digit in the ones place, we make a two-digit number. In a two-digit number, the tens place can have any digit from 1 to 9.’ Ask students to share different two-digit numbers they can make. Have them use their whiteboards if needed. Invite students to think–pair–share about the smallest number they can make. ’What is the smallest two-digit number you can make? How did you figure it out?’ (10 is the smallest two-digit number. 1 is the smallest digit that can go into the tens place and 0 is the smallest digit that can go into the ones place.) Write 10. ‘What is the biggest two-digit number you can make? How did you figure it out?’ (It’s 99. Nine is the biggest digit. It makes the most tens and the most ones, so we can put it in both places.) Write 99 to the right of 10. Then draw a < symbol. ‘Let’s read this comparison number sentence together.’ (10 is less than 99.) If time allows, extend student thinking with the following discussion. ‘99 is the largest two-digit number because it has a 9 in the tens place and a 9 in the ones place.’ Write 99<100 and read it aloud. ‘Even though 99 has 9 in both places, it is not greater than all numbers. 100 has the smallest digits, 1 and 0, but it is greater than 99. That’s because the 1 is in a place we will learn about another time: the hundreds place!’”

• Module 6, Lessons 11 and 12 engage students with 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 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). Lesson 11: Name equal shares as halves or fourths, Learn, Halves and Fourths, students look at pictures of different foods and determine if each is partitioned into halves or fourths. “Prompt students to open their student book to the foods partitioned into halves and fourths. Invite students to think–pair–share about the foods that are partitioned in half. ‘Which foods are partitioned in half? Circle them.’ (The watermelon, sandwich, hot dog, and apple are cut into halves. They all have 2 equal parts, or shares.) Then have students think–pair–share about the foods that are not partitioned into halves. ’How are the cracker and the pie partitioned? How do you know?’ (They are in 4 equal parts. That’s fourths.) Ask students to look at the crackers that are shaped like a square and a circle at the bottom of the page. ‘Draw a line in the square cracker to make halves. Color 1 half of the cracker. Draw two lines in the circle cracker to make fourths. Color 1 fourth of the cracker.’ Invite a few students who partitioned the crackers differently to share their work.” Lesson 12: Partition shapes into halves, fourths, and quarters, Learn, Partitioning Shapes, students work with partners to partition circular and rectangular shapes into halves and fourths. “Make sure each partner has the Partition the Snack removable inserted into their personal whiteboard. Model the following directions. Partner A partitions all of the food pictures, some into halves and some into not halves. Partner B points to each picture and says ‘Halves’ or ‘Not halves’ and explains their thinking. Partners erase their whiteboards. Then partner B partitions all of the food pictures, some into fourths and some into not fourths. Partner A points to each picture and says ‘Quarters’ or ‘Not quarters’ and explains their thinking. Partner A can also say, ‘Fourths.’ Partners erase their whiteboards. Allow 1–2 minutes for students to practice with halves, and 1–2 minutes to practice with fourths. Encourage students to find as many ways as they can to partition the foods. Use the following questions to assess and advance thinking: How do you know this is partitioned into halves (or fourths or quarters)? How do you know that this is not partitioned into halves (or fourths or quarters)? Where do you see a half? Where do you see a fourth (or quarter)? Gather the class. Invite students to choose one food item. ‘Partition your food into halves. Color 1 half.’ Have students hold up their whiteboards to share their work. Give feedback. Repeat the process with quarters.” In the Debrief, students determine if pizzas have been partitioned equally into halves or fourths.

The materials reviewed for Eureka Math² Grade 1 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. The instructional materials devote at least 65 percent of instructional time to the major clusters of the grade. 

• The number of modules devoted to major work of the grade (including assessments and supporting work connected to the major work) is 6 out of 6, approximately 100%.

• The number of lessons devoted to major work of the grade (including supporting work connected to the major work)  is 121.75 out of 140, approximately 87%. 

• The number of days devoted to major work of the grade (including assessments and supporting work connected to the major work) is 125.5 out of 146, approximately 86%.

A lesson-level analysis is most representative of the instructional materials as the lessons include major work and supporting work connected to major work. As a result, approximatley 87% of the instructional materials focus on major work of the grade.

The materials reviewed for Eureka Math² Grade 1 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 

Materials are designed so supporting standards are connected to the major work standards and teachers can locate these connections on a tab called, “Achievement Descriptors and Standards” within lessons. Examples include:

• Module 1, Topic A, Lesson 2: Organize and represent data to compare two categories, Learn,  Represent Data with Cubes connects the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.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 <). Students graph and compare two categories of data by placing cubes on number paths. “Display two number paths on a piece of chart paper as shown. Distribute a cube to each student. ‘As I pass out the cubes, let’s count them together. Why did we count up to ___ (number of students present in class)?’ (That’s how many students we have.) ‘Let’s use a cube to show each student’s choice. Use your cube instead of your hand this time to make your choice. Which do you like better: listening to stories or listening to music?’ Use sticky notes to label the number paths with the words Music and Stories. ‘We will use two number paths: one to show who likes listening to music and the other to show who likes listening to stories.’ Call up students who chose listening to music. Have them place their cubes one at a time, starting at 1, on the music number path. Emphasize the count by having the class say the number as each student places their cube. Have students reiterate the total and use a sticky note to label it as shown. Repeat the process with the stories number path for students who chose listening to stories. When students finish, invite them to look at the final graph. If spaces are skipped or cubes are misaligned, work with students to make corrections. As a class, discuss what each cube means: Each cube stands for one student choice. ‘When we organize our choices on number paths, line up the number paths, and add labels, we create a graph.’ Label the representation with the word graph on a sticky note to connect the new term to the visual representation. Then add a sticky note to title the graph We Like Music or Stories as shown. ‘Adding a title to our graph tells us what the graph is about.’ Lead a class discussion about what students notice about the graph. ‘How does the graph help us organize our choices?’ (Our choices are shown in lines. Each cube is on a square, so we make sure to count it.) ‘What does the graph show us about our choices?’ (We can see if more students chose music or stories. There are more cubes on the music path.) Have students think-pair-share about the following question. ‘How do we know that more of us like listening to music than listening to stories?’ (The line of cubes for music is longer. 13 is more than 11. Not all the cubes on the stories path have a match (or a partner). There are extra cubes on the music path.) ‘Remember, we can say that 13 is more than 11 another way: 13 is greater than 11. Say that with me.’ (13 is greater than 11.) Write the comparison statement to describe the two totals. Write a comparison number sentence that includes the > symbol as shown. ‘Mathematicians draw a symbol to write is greater than.’ Ask students to read the number sentence. Point to each part as they read.”

• Module 2, Topic E, Lesson 20: Add or subtract to make groups equal, Learn, Cracker Comparison, connects the supporting work of 1.MD.4 (Organize, represent, and interpret data with up to three categories; ask and answer questions about the total number of data points, how many in each category, and how many more or less are in one category than in another) to the major work of 1.OA.1 (Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions) and 1.OA.7 (Understand the meaning of the equal sign, and determine if equations involving addition and subtraction are true or false). In the activity, students look at objects (crackers) organized into two groups and the mathematics that would need to be done to make the number in each group equal. “Have students turn to the picture of crackers in their student books. Display the picture of Zoey and Adrian. ‘Zoey and Adrian are packing a snack. What is different about their crackers?’ (Zoey has 6 crackers. Adrian has 9 crackers.) ‘What is the same about their crackers?’ (They both have the same kind of cracker. They have 6 crackers that match up. They are lined up.) ‘We can match Zoey’s 6 crackers to 6 of Adrian’s crackers. (Draw a line to match up each pair of crackers.) What could they do to make sure they have the same number of crackers? Turn and talk.’ Ask students to draw on their whiteboards to show two ways that Zoey and Adrian can have the same number of crackers. They do not need to write a number sentence yet. Look for students who use strategies similar to those modeled in Launch. Invite two students to explain their ideas. (I drew 3 more crackers for Zoey. Now they both have 9 crackers. I crossed off 3 of Adrian’s crackers. Now they both have 6 crackers.) Ask students to look at their work to compare it with the two sample strategies given. Some students may choose to revise or complete their work. ‘What number sentence can we write to show what the first student did?’ (6+3=9). Have students record the number sentence above Zoey’s crackers. Then use the following process to guide students to represent what the second student did by using the order that matches the picture. ‘Zoey has 6 crackers. (Write 6.) Adrian has 9 crackers. We take away 3. (Write = 9-3.) Look at the number sentence we just wrote: 6=9-3. 6 is the same total as 9 minus 3. Is that true? How do you know?’ (Yes, it is true. 9 minus 3 equals 6.)”

• Module 5, Topic A, Lesson 1: Tell time to the hour and half hour by using digital and analog clocks, Learn, Hours and Minutes, connects the supporting work of 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). “Show students 1 o’clock on the analog clock only. (Point to the red hand.) ‘The short hand is the hour hand. It tells the hour. (Point to the blue hand.) The long hand is the minute hand. It tells the minutes.’ Turn on the digital clock as well. ‘This is a different type of clock. It shows the time using only numbers. The numbers to the left of the dots tell the hour. (Point to the 1 on the digital clock.) The numbers to the right of the dots tell the number of minutes.’ (Point to the 00 on the digital clock.) Tell students that both clocks show 1 hour and 0 minutes. Help them read the time on each clock as 1 o’clock. Tell students that as time passes, the hands on the first clock (the analog clock) move, but the numbers on the second clock (the digital clock) just change. ‘Watch and see what happens on each clock as time passes. Let’s count minutes.’ Slowly move the minute hand from 1:01 to 1:30. Have the class chorally count the minutes. (1 minute, 2 minutes, … , 29 minutes, 30 minutes.) Point to the analog clock that shows 1:30. ‘What did the hands do on this clock as we counted?’ (The minute hand moved a little bit at a time. It went from the top of the clock to the bottom of it. The hour hand only moved a little. Now it’s past the 1, but not to the 2.) Reset the clock to 1 o’clock. ‘As time passes, the minute hand moves forward one tick mark at a time. Each tick mark represents 1 minute. Watch the blue minute hand. Slowly move the minute hand from 1:00 to 1:05. The hour hand moves too. As minutes go by, the hour hand moves slowly from one number on the clock to the next. Watch the red hour hand.’ Slowly move the minute hand to 1:30. ‘Now the hour hand is between two numbers, or hours. The minute hand points straight down to the 6. When the hands are in this position, we say the first number for the hour and read the time as one thirty.’ Point to the digital clock that also shows 1:30. ‘What did the numbers on this clock do as we counted?’ (They changed. The minutes went from 00 up to 30. They went up by 1 each time.) ‘What time does the clock show?’ (1:30) ‘Both clocks started at 1 o’clock. We counted 30 minutes from 1 o’clock to 1:30. Now the clocks show 1:30. Let’s keep counting until the minute hand moves all the way around the clock.’ (Point to the picture of the analog clock.)  Slowly move the minute hand from 1:30 to 2 o’clock. Have the class chorally count the minutes. (31 minutes, 32 minutes, … , 59 minutes, 60 minutes) ‘What time do the clocks show now? How do you know?’ (2 o’clock; The hour hand is pointing at the 2 and the minute hand is on the 12. There is a 2 and two zeros on the clock with only numbers.) Confirm that both clocks show 2 o’clock. (Point to the digital clock.) ‘On this clock, after the minutes show 59, they start over at 0. It shows 1:59 and then 2:00. This happens because there are 60 minutes in 1 hour. How many minutes are in an hour?’ (60 minutes) (Point to the analog clock.) ‘On the other clock, when the minute hand goes all the way around the clock, the hour hand arrives at the next number, or hour. Now the hour hand is pointing to 2.’”

• Module 6, Topic F, Lesson 31: Add to make 100, Learn, Find the Total, connects the supporting work of 1.G.1 (Distinguish between defining attributes versus non-defining attributes…) to the major work of 1.NBT.4 (Add within 100, including adding a two-digit number and a one-digit number…). “Students find the number of objects in a collection that totals 100. Ask students to turn to the picture of candies in their student book. Tell them to find the total number of candies and record their thinking. Encourage them to confirm their total by finding it a second way. Circulate and identify student work samples that show a variety of ways to make 100.”

The instructional materials reviewed for Eureka Math² 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. 

Grade 1 lessons are coherent and consistent with the Standards and teachers can locate standard connections on a tab called, “Achievement Descriptors and Standards” within lessons. Examples include:

• Module 2, Topic A, Lesson 3: Subtract 1 or subtract 1 less than the total, Launch, connects the major work of 1.OA.C (Add and subtract within 20) with the major work of 1.OA.D (Work with addition and subtraction equations). Students subtract 1 from a number and make a subtraction equation. “Gather students. Display and read the following bus story aloud. ‘10 people are on the bus. 1 person gets off the bus. How many people are on the bus now?’ Have pairs turn and talk about the story. Give them time to solve the problem by using their choice of the School Bus Stories mat, Unifix Cubes, fingers, or drawings. Have students record a number sentence on their whiteboard. ‘How many people are on the bus now? How did you figure it out?’ (9. I put up 10 fingers and put 1 down. 9. I put 10 cubes on the bus and took 1 away. 9. I just know 9 is 1 less than 10.) ‘What number sentence represents, or shows, this story?’ (10-1=9) Record and display 10-1=9 on chart paper to start a list of number sentences that show subtracting 1. Repeat the process with another bus story. ‘9 people are on the bus. 1 person gets off the bus. How many people are on the bus now?’ Have students reflect on the two number sentences listed and invite students to think-pair-share. ‘What do you notice about these number sentences?’ (Both show minus 1. The answer is 1 less than the number we started with.) Transition to the next segment by framing the work. ‘Today, let's solve a set of problems like these and see what we notice about the answers. As we work, think about what statement we can make.’”

• Module 5, Topic E, Lesson 24: Decompose an addend to make the next ten, Land, Debrief, connects the major work of 1.OA.D (Work with addition and subtraction equations) to the major work of 1.NBT.C (Use place value understanding and properties of operations to add and subtract). Students engage in discussion after working with problems where they practiced decomposing addends to make ten. “Display 18+12=  solved three different ways. Show one way at a time. The first way is by adding like units. The second way is by adding tens first. The third way is to make the next ten. In all three ways, one or both addends were decomposed. Invite students to analyze each work sample by using a variation of the Five Framing Questions routine. The responses provided for the following questions show a possible answer for each work sample. Have students notice and organize. ‘How did this student find the total?’ (They broke up both addends into tens and ones. They added tens, then ones, then they put those totals together. They broke up the 12 into 10 and 2. They added 18 and 10 first. Then they added 2 more. They broke up 12 into 2 and 10 so they could make the next ten with 18. 18 and 2 makes 20, plus 10 more makes 30.) Display all three samples at the same time. Help students reveal the strategies. ‘Let’s focus on breaking apart addends. Where do you see addends broken apart in the work?’ (In the first one they broke up 18 and 12. In the others they broke up only 12. All of the addends that are broken up get put into tens and ones.) Help students to distill the information and know how these strategies help them to add. ‘How do you think breaking apart addends helped these students?’ (You can make easier problems by breaking apart numbers. Breaking apart numbers lets you make the problems smaller.) Guide students to further know how these strategies help them. ‘What are some ways to make an easier problem?’ (You can break numbers into tens and ones to add in different ways. You can add tens with tens, ones with ones, and then put them together. You can add the tens from the second number to the first number, then add the ones. You can think about what the next ten is and make it.)”

• Module 6, Topic A, Lesson 1: Name two-dimensional shapes based on the number of sides, Learn, Cut and Sort, connects the supporting work of 1.MD.C (Represent and interpret data) to the supporting work of 1.G.A (Reason with shapes and their attributes). Students sort and organize shapes based on the number of sides each shape has. “Partner students and make sure that each pair has the Shape Cut removable, the two-page Shape Sort removable, and scissors. Partner A cuts the Shape Cut removable on the dotted line and gives one piece to partner B. Make sure the Shape Sorts pages are side by side where both partners can reach them. ‘First, cut on the black lines. Then cut out each of the four shapes. Use the gray parts to cut your own shapes with 3, 4, 5, or 6 sides.’ Direct partners to sort their shapes. ‘Work together to sort the shapes. Count the number of sides on each shape. Place the shapes where they belong on the Shape Sort.’ (Point to the word Triangle.) ‘We know that closed shapes with 3 straight sides are called triangles.’ Hold up a shape from the Triangle category and have the class count the sides chorally. ‘Check your work to be sure the shapes in this group are triangles. Show thumbs-up when you are ready. (Point to the word Quadrilateral.) All closed shapes with 4 straight sides are called quadrilaterals, although sometimes we know them by other names. What can we call all shapes with 4 sides?’ (Quadrilaterals) Hold up each shape from the Quadrilateral category and have the class count the sides chorally. Have students check their work. Repeat the process with the pentagons and hexagons. Consider having students glue their shapes on the Shape Sorts and displaying them.”

• Module 6, Topic C, Lesson 14: Tell time to the half hour with the term half past, Learn, Half Past, connects the supporting work of 1.MD.B (Tell and write time) to the supporting work of 1.G.A (Reason with shapes and their attributes). Students practice telling time to the half hour by using both analog and digital clocks. “Display the clock with no hands. ‘What shape is a clock?’ (Circle) Display the clock partitioned in half. ‘What shape is half of a circle? (Half-circle) Point to the vertical line from 12 to 6. Invite students to point out the half-circles on the clock. ‘Each time the minute hand goes around the whole circle, we count 1 hour. When the minute hand goes around a half-circle, we count half of an hour.’ Using the digital interactive, show 2 o’clock on the analog clock only. ‘What time does this clock show?’ (2 o’clock) ‘Yes, let’s go past 2 o’clock until the minute hand makes a half-circle and shows half past 2, or half an hour past 2 o’clock.’ Move the minute hand one minute at a time to 2:30 as students chorally tell the time (2:01, … , 2:15). Pause at 2:15 and have students reflect on the movement of the hands. ‘What is happening with the minute hand? What happened to the hour hand?’ (The minute hand is moving past 2 o’clock one minute at a time. The hour hand is moving, too, but slower than the minute hand is moving.) ‘What do you notice about the green part?’ (The green part gets bigger as the hands move. The green part is a quarter-circle now.) ‘Does the clock show half past 2 o’clock now? How do you know?’ (No, the minute hand hasn’t made a half-circle yet.) Repeat the process from 2:15 to 2:30. ‘What do you notice about the hands and the green part now?’ (The green makes a half-circle. The hour hand is between the 2 and the 3. The minute hand is on the 6 now.) ‘Does the clock show half past 2 now? How do you know?’ (Yes, the minute hand went past 2 o’clock and made a half-circle.) ‘This clock shows half past 2. The minute hand started at 12 and made a half-circle around the clock. That tells us that half of an hour went by. What time does the clock show at half past 2?’ (2:30) Show 2:30 on the digital clock as well. (Point to the digital clock.) ‘At 2:30 this clock shows 2 hours and 30 minutes.’ (Point to the 2 and then to the 30.) (30 minutes is the same as half of an hour.) Write half past where students can see it for the remainder of the lesson. ‘The person who wrote the note said half past 2. What time is half past 2?’ (2:30) Show 3:00 on the analog clock. ‘Talk to your partner. What time do you think it will be at half past 3?’ Show 3:30 and ask the class to state the time chorally. ‘Half past 3 is the same as 3:30. The minute hand started at 12 and made a half-circle, or went 30 minutes, around the clock.’ As time allows, show other times, such as 12:30, and ask the class to chorally state the time both ways: first as 12:30 and then as half past 12.”

The materials reviewed for Eureka Math² 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.

Content from future grades is identified within materials and related to grade-level work. These references are consistently included within Topic and Module Overviews and less commonly found within teacher notes at the lesson level. Examples include:

• Module 2, Topic B: Relate and Distinguish Addition and Subtraction, Topic Overview, connects 1.OA.D (Work with addition and subtraction equations) to writing equations to represent and solve problems in later grades. “At this point in grade 1, students usually solve by making drawings that directly model the problem. Some students may solve problems by using fingers or manipulatives and then draw to record their method. As part of the RDW process, they also write a number sentence to record their thinking. Practice with writing the number sentences is important because, as students get older, they write an equation based on their drawing and solve the equation to find the solution rather than relying solely on their drawing to solve.”

• Module 4, Topic B, Lesson 8: Draw to represent a length measurement, Learn: Draw to Represent connects 1.OA.A (Represent and solve problems involving addition and subtraction) to other models and strategies in later grades. “The look and feel of the drawings used in this lesson are important for students to become familiar with moving forward because they are similar to a tape diagram, which they will use regularly in later grades.”

• Module 6: Attributes of Shapes · Advancing Place Value, Addition, and Subtraction, Module Overview, Part 1: Attributes of Shapes, After This Module, connects 1.G.A (Reason with shapes and their attributes) to work done in Grade 2, Module 3. “Students begin using the number of angles in a shape as a defining attribute of flat shapes. They use the number of faces, edges, and vertices as defining attributes of solid shapes. Fraction work expands from working with halves and fourths to include thirds. Students refine their understanding of equal shares as they see that equal shares are the same size, but not always the same shape. Grade 2 students relate fractions to telling time by using the language quarter past and quarter to.” (2.MD.7, 2.G.A)

• Module 6, Topic D, Lesson 16: Count and record totals for collections greater than 100., Launch, Promoting the Standards for Mathematical Practice, connects the work of 1.NBT.B (Understand place value) to work in Grade 2. “Students formally extend their understanding of place value to include the unit of hundreds in grade 2. However, they can still use place value concepts to precisely describe how to read and write three-digit numbers.” 

Materials relate grade-level concepts from Grade 1 explicitly to prior knowledge. These references can be found consistently within Topic and Module Overviews and less commonly within teacher notes at the lesson level. Examples include:

• Module 1, Topic D, Lesson 18: Determine whether number sentences are true or false, Learn, Teacher Note, connects 1.OA.D (Work with addition and subtraction equations) to prior learning in Kindergarten. “Students decomposed and composed 5 in kindergarten. The two-part expressions that equal 5 are intentionally used in this lesson so that students can extend their thinking to equality between expressions. Using familiar combinations will allow them to attend to new, more complex mathematical concepts.” (K.OA.A)

• Module 2, Topic A: Reason About Take From Situations, Topic Overview, connects 1.OA.C (Add and subtract within 20) to work done in Kindergarten. “In kindergarten, students worked extensively with the 5+n pattern. In topic A, they use the familiar unit of 5 in a subtraction context, taking away 5 fingers all at once. This action supports students to then solve problems by taking away 4 and 6 all at once. Taking away a part all at once is foundational to the Level 3 subtraction strategy known as take from ten.” (K.OA.A)

• Module 5: Place Value Concepts to Compare, Add, and Subtract, Module Overview, Before This Module, connects 1.NBT.B (Understand place value) to prior learning in Kindergarten Module 6: Place Value Foundations. “Students begin to develop place value understanding when they come to see that teen numbers are composed of 10 ones and some more ones. They do not formalize the notion of ‘a ten’ as a unit. Students also count to 100 by tens and by ones.” In addition, it connects the prior learning in Grade 1, Module 3: Properties of Operations to Make Easier Problems. “Students rename groups of ten ones as units of ten. They come to see that all two-digit numbers are composed of tens and ones.” (K.NBT.A)