1st Grade - Gateway 2

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

All units begin with a Unit Organizer, Planning for Rich Math Instruction. This component indicates where conceptual understanding is emphasized within each lesson of the Unit. The Focus portion of each lesson introduces new content, designed to help teachers build their students’ conceptual understanding through exploration, engagement, and discussion. The materials include problems that develop conceptual understanding throughout the grade level, especially where called for in the standards. Examples include:

• Lesson 1-6, Comparing Numbers, Focus: Comparing and Ordering Numbers, students use number cards from 1-15 to compare numbers and order sets of numbers. Students mix their cards up, draw two cards, and use the class number line to decide which number is larger. Students are encouraged to, “Use comparative language such as ‘8 is larger than 2, and 12 is smaller than 15.” This activity supports conceptual understanding 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 3-1, Parts-and-Total Number Stories, Focus: Introducing Domino Addition, students represent the number of dots on dominoes with parts-and-total diagrams. For example, for a domino with 3 and 5 dots students write Part: 3, Part: 5, and Total: 8 on the diagram in their math journal and then write the corresponding number sentence. “Complete a parts-and-total diagram for the domino. Point out that one part of the domino has 3 dots and the other part has 5 dots - so the domino has 8 dots in all.” This activity supports conceptual understanding of 1.OA.6, “Use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing unknowns in all positions.”

• Lesson 5-1, Introducing Place Value, Focus: Exchanging Base-10 Blocks, students represent numbers using base-ten blocks. “Display 1 long and 15 cubes on your mat. Ask: What number is shown? Discuss how children can be sure. Demonstrate the following two exchanges, or trades, starting with 1 long and 15 cubes each time: Trade the long for 10 cubes, then count the total number of cubes to get to 25. Trade 10 cubes for 1 long and place the long in the tens column. As you trade, emphasize that you are making another ten (1 long) from 10 ones (10 cubes). There are now 2 longs and 5 cubes. Ask: What number is shown? What does the 2 represent? What does the 5 represent?” This activity supports conceptual understanding of 1.NBT.2, “Understand that the two digits of a two-digit number represent amounts of tens and ones.” 

• Lesson 7-6, Exploring Attributes, Fractions, and Salute! Focus: Making an Attribute Train, one student brings an attribute block to the front of the room and is designated the conductor. They choose a child to join the train and that student must bring a block to add to the train that differs from the conductor’s block in only one way, “For example, a child with a large, thick, blue triangle may choose a child with a large, thin, blue triangle, or a large, thick blue square. Each child who joins the train chooses the next child.” This activity supports conceptual understanding of 1.G.1, “Distinguish between defining attributes versus non-defining attributes, build and draw shapes to possess defining attributes.”

• Lesson 8-11, Focus: Adding and Subtracting 10 Mentally, students apply strategies for adding or subtracting 10. “Discuss how children found their answers to the Math Message (35 cents). Emphasize strategies, including visualizing a number grid and moving down a row from 25 to 35, thinking about adding a long to base-10 blocks representing 25, and adding 1 to the tens digit of 25.” This activity supports conceptual understanding of 1.NBT.5, “Given a two-digit number, mentally find 10 more or 10 less than the number, without having to count to explain the reasoning used.”

Home Links and Games provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

• Lesson 4-3, More Length Measurement, Math Journal, students independently practice measuring objects such as their desktop using one new pencil as the unit. Then students draw a picture or write the name of the measured object and record its measurement, “Draw pictures or write the names of 4 objects. Measure each object with a new pencil. Record your answer.” This activity supports the conceptual understanding of 1.MD.2, “Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.”

• Lesson 5-8, Exploring Base-10 Exchanges, Lengths, and Path Measurement, Focus: Introducing Base-10 Exchange, students play with a partner practicing exchanging ones for tens after rolling the die to determine how many base-10 blocks to get. The first student to get 10 longs wins, “As children play, be sure to ask questions that reinforce place-value concepts.” This activity provides practice of conceptual understanding of 1.NBT.2, “Understand that the two digits of a two-digit number represent amounts of tens and ones.”

• Lesson 8-2, Halves, Math Journal, Problem 2, students partition pictures of pancakes and crackers in equal shares and explain how they know the share is equal. “Show how to share 1 cracker between 2 people.” This activity supports the conceptual understanding 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.”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

All units begin with a Unit Organizer, Planning for Rich Math Instruction. This component indicates where procedural skill and fluency exercises are identified within each lesson of the Unit. The Mental Math Fluency exercises found at the beginning of each lesson develop fluency with basic facts and other skills that need to be automatic while engaging learners. The Practice portion of the lesson provides ongoing practice of skills from past lessons and units through activities and games. Examples include:

• Lesson 2-1, Introducing the Strategy Wall, Focus: Introducing Roll and Total, students take turns with a partner to roll one numeral die and one dot die. “This encourages children to start with the numeral die and count on the number of dots, thus moving beyond counting all to find sums.” Students should recognize that it is more efficient to count on from the larger number being added. This activity provides an opportunity for students to develop fluency of 1.OA.5, “Relate counting to addition and subtraction.”

• Lesson 3-3, Exploring Counting, Matching Pairs, and Ordering by Length, Focus: Counting Large Numbers of Pennies, groups of students are given a container of at least 50 pennies, estimate the total, then count and record the number of pennies. “Encourage children to work together to count the pennies and to check each other’s counts. Then have them record their group’s counting strategy in the journal using pictures or words.” This activity provides an opportunity for students to develop fluency of 1.NBT.1, “Count to 120, starting at any number less than 120.”

• Lesson 3-6, Counting to Add and Subtract, Focus: Introducing Addition on the Number Line, students represent and make sense of word problems by drawing hops on a number line. “Cynthia had 8 model cars. She got 3 more model cars. How many model cars does Cynthia have now?” Teachers encourage children to represent and make sense of the problem by drawing hops on the first number line. This activity provides an opportunity for students to develop fluency of 1.OA.6, “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.”

• Routine 6: Math Any Time Routine, the class daily schedule can be used to practice time concepts on individual student clocks. “How long does lunch last? It is 9:00 a.m. now, how long will it be until we start math? Which activity takes the shortest amount of time today?” This activity provides a continuous opportunity for students to develop fluency of 1.MD.3, “Tell and write time in hours and half-hours using analog and digital clocks.”

Math Boxes, Home Links, Games, and Daily Routines provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade. Examples include:

• Lesson 2-3, More Decomposing Numbers with 10, Home Link, Question 1, students find pairs of numbers that add to 10. “Count up by 1s. 7, 8, 9, ___, ___, ___, ___, ___, ___, ___, ___.” This provides an opportunity for students to independently demonstrate the procedural skill of 1.NBT.1, “Count to 120 starting at any number less than 120.”

• Lesson 8-1, Building Shapes with Defining Attributes, Practice: Math Journal 2, Question 4, students write fact families from fact triangles (11, 6, and 5) dominos (8 and 6). “How can 9+3=12 help you solve 12-9?” This activity provides an opportunity for students to independently demonstrate the procedural skill of 1.OA.6, “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.”

• Lesson 8-2, Halves, Practice: Math Journal 2, Question 4, students practice addition and subtraction. “Use your number grid. Add. 17+10= ____, 17+20= ____, 17+30= ____.” This activity provides an opportunity for students to independently demonstrate the procedural skill of 1.NBT.4, “Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10.”

• Lesson 9-4, Exploring Broken Calculators, Fractions, and Facts, Practice: Math Journal 2, students complete a “My Facts Inventory Record.” Students are given addition facts such as 10+2, then check a box if they know it or don’t know it, then explain how they can figure it out, “Encourage them to use more sophisticated and efficient strategies when applicable (for example, substituting near doubles or making 10 for counting on) for remaining facts that they do not know.” This activity provides an opportunity for students to independently demonstrate the procedural skill of 1.OA.6, “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.”

The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Materials include multiple routine and non-routine applications of mathematics throughout the grade level. Focus activities introduce new content, provide routine exercises, review recent learning, and provide challenging problem-solving tasks that help build conceptual understanding, procedural skill and fluency, and application of mathematics. Open Response lessons provide challenging problems that involve more than one strategy or solution. Home-Links relate to the Focus activity and provide informal mathematics activities for students to do at home. Examples of routine and non-routine applications of the mathematics include:

• Lesson 3-2, Number Story Strategies, Practice: Modeling Number Stories, Home-Link, students write number models to solve stories. Problem 1, “Walt was at the carnival. He had 8 carnival tickets and 2 pens. He traded 4 tickets for 1 more pen. How many tickets does Walt have now? How many pens does Walt have now?” This activity provides the opportunity for students to apply their understanding 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.”

• Lesson 4-4, Measuring a Marker, Focus: Solving the Open Response Problem, students work with a partner to analyze measurement strategies. Math Masters, p. 97, Problem 2, “Here is how four children used blocks to measure the length of a marker. Who made the best measurement? Write a note to convince a friend that you are right.” Students are given 4 pictures of makers with blocks pictured above each marker to show how each one was measured. Students apply their understanding of 1.MD.2, “Express the length of an object as a whole number of length units, by laying multiple copies of a shorter object (the length unit) end to end; understand that the length measurement of an object is the number of same-size length units that span it with no gaps or overlaps.”

• Lesson 4-10, Adding Three Numbers, Focus: Adding Three Numbers, students add three numbers from School Supply Cards. “Our class has 7 pencils, 4 pens, and 3 crayons. How many writing tools do we have in all?” Students apply their understanding of 1.OA.2, “Solve word problems that call for addition of three whole numbers whose sum is less than or equal to 20.”

• Lesson 5-10, Comparison Number Stories, Focus: Finding How Much More or Less, students solve comparison number stories using diagrams. “Alberto has 12 cents. June has 7 cents. Who has more money? How much more money?” Students apply their understanding 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.”

Materials provide opportunities for students to independently demonstrate multiple routine and non-routine applications of the mathematics throughout the grade level. Independent Problem Solving provides “additional opportunities for children to apply the content they have learned during the section to solve non-routine problems independently. These problems often feature: applying math in the real world, multiple representations, drawing information or data from pictures, tables, or graphs, and opportunities for children to choose tools to support their problem-solving.” Examples of independent demonstration of routine and non-routine applications of the mathematics include:

• Independent Problem Solving 2a, “to be used after Lesson 2-5”, Problem 1, students make combinations of 8. “A dog park has 8 dogs in it. Some dogs are large and some are small. How many of each could there be? Draw a picture to show one way you could have 8 dogs.” This activity provides the opportunity for students to independently demonstrate an understanding 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.”

• Independent Problem Solving 3b, “to be used after Lesson 3-7”, Problem 1, students solve a routine word problem. “Eisa had 13 pencils. She lost 6 pencils. How many pencils does Eisa have now? Use pictures or words to show your thinking. Use pictures or words to show a different way you could solve the number story.” This activity provides the opportunity for students to independently demonstrate an understanding 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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.”

• Independent Problem Solving 4b, “to be used after Lesson 4-10”, Problem 2, students use addition strategies to solve a problem. “Kierre has 6 red grapes, 4 green grapes, and 6 purple grapes. How many grapes does Kierre have in all? Which numbers did you add first? Why did you add these first? What could you add first instead?” This activity provides the opportunity for students to independently demonstrate an understanding 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, e.g., by using objects, drawings, and equations with a symbol for the unknown number to represent the problem.”

• Independent Problem Solving 9b, “to be used after Lesson 9-8”, Problem 2, students compare weights of items by using place value strategies. “Look at your Animal Cards. Choose a pair of animals whose total weight is heavier than Pair 1 but lighter than Pair 2. Write them in the middle section below. Pair 1: A flamingo and an octopus. My Pair. Pair 2. A penguin and a starfish. Write or show how you decided.” This activity provides the opportunity for students to independently demonstrate an understanding of 1.NB.3, “Compare two two-digit numbers based on meanings of the tens and ones digits, recording the results of comparisons with the symbols >, =, and <.”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

All three aspects of rigor are present independently throughout the grade. Examples where materials attend to conceptual understanding, procedural skills, and fluency, or application include:

• Lesson 3-8, Skip Counting to Add and Subtract, Focus: Using Number-Grid Counting to Add and Subtract, students solve number stories by skip counting on a number grid, “Tell children the following number story: Justin’s teacher gives out stickers for good behavior. At the beginning of the day, Justin had 0 stickers. During the day, he earned 10 stickers. How many stickers does Justin have at the end of the day? Have children share solutions to the problem.” This activity provides the opportunity to apply an understanding of 1.OA.3, “Apply properties of operations as strategies to add and subtract.”

• Lesson 4-8, Combinations of 10, Focus: Fact Strategy Review, students discuss addition facts and note which facts they know well on a Facts Inventory Record, “Explain that addition facts are two numbers from 0 to 10 and their sum. Point out that children can use the strategies on the Strategy Wall to solve addition facts. Record children’s ideas about adding 0 on the Strategy Wall.” This activity develops the procedural skill of 1.OA.6, “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10.”

• Lesson 5-2, Digits and Place Value, Focus: Investigating Base-10 Block Patterns, students make place-value exchanges and discuss various ways to represent numbers, “Tell children that today they will explore patterns in numbers using both base-10 blocks and calculators. Display the following with your Tens-and-Ones Mat as children follow along on their own mats. 1. Display 9 cubes in the ones column. 2. Add 1 cube to the ones column. 3. Exchange the 10 cubes for 1 long and put it in the tens column. This activity develops a conceptual understanding of 1.NBT.2, “Understand that the two digits of a two-digit number represent amounts of tens and ones.”

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

• Lesson 2-1, introducing the Strategy Wall, Focus: Introducing the Turn-Around Rule, students discover and define the turn-around rule for addition. “Solve. Show your work. Use drawings, numbers, or words. 1. On Monday, Ellie found 2 pennies. On Tuesday, Ellie found 3 pennies. How many pennies did Ellie find in all? 2. On Monday, Tommy found 3 pennies. On Tuesday, Tommy found 2 pennies. How many pennies did Tommy find in all?” After solving, students discuss with a partner. “Help children recognize that both problems involve putting together two parts, which is called adding. They should also observe that both problems have the same numbers and the same total, or sum, but the order of the numbers being added is different.” Students develop the procedural skills of 1.OA.6, “Add and subtract within 20, demonstrating fluency for addition and subtraction within 10,” and application 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.”

• Lesson 6-6, Introducing Making 10, Focus: Math Message and Developing the Making-10 Strategy, students first show how they represent numbers on a double ten frame, then they represent the making-10 strategy, “How could you show 15 on a double ten frame? How about 18? 19? Record your thinking on your slate. Display a double ten frame. Have children use their own double ten frames and counters to share their thinking. Although children may represent the numbers in the Math Message in a variety of ways, emphasize filling one ten frame with ten and then repeating the remaining ones on the second ten frame. Generalize this idea by asking: How can you represent teen numbers?” Students develop conceptual understanding of 1.NBT.2, “Understand that two digits of a two-digit number represent amounts of tens and ones,” and procedural skill with 1.NBT.1, “Count to 120, starting at any number less than 120.”

• Lesson 8-8, time to the Half Hour, Focus: Math Message and Introducing Time to the Half Hour, students are introduced to half-past an hour and shade half of a clock face, “Draw the clock face, and shade half of the clock. How much time has passed if the minute hand begins at 12 and goes through all of the shaded parts? Children share their drawings. 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.” Students develop conceptual understanding of 1.G.3, “Partition circles and rectangles into two and four equal shares,” and procedural skills with 1.MD.3, “Tell and write time in hours and half-hours using analog and digital clocks.”

The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice). 

Materials provide intentional development of MP1 to meet its full intent in connection to grade-level content. Students make sense of problems and persevere in solving them as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 2-8, Change-to-More number Stories, Focus: Introducing Change-to-More Diagrams, students use change-to-more diagrams to add and determine if their answers make sense. “List some of the children’s predictions and have them explain their thinking. Ask the class whether the predictions seem reasonable. For example, predicting a sum that is smaller than one of the numbers being added would not be reasonable.” 

• Lesson 6-9, Understanding Equivalence, Focus: Illustrating Equivalence, students monitor their progress as they learn the word equivalent and that numbers can have different names like people or things. “Ask children to list the addition facts that have sums of 7. Each fact contains an equivalent name for 7: 4+3, 2+5, 1+6, 0+7=7 and so on.” “Ask children if they can think of another way to show 7 with the counters.”

• Lesson 8-9, Review: Data, Focus: Math Message, students analyze and make sense of problems when shown a tally chart with missing tallies for one of three categories. “Mr. Chan’s class took a survey to figure out which pet is the favorite. They made a tally chart, but the tallies for Turtle got erased. If 19 children voted, how many voted for Turtle? What do you need to do to solve this problem? Record your answer, and explain how you found it.” 

• Independent Problem Solving 8a, “to be used after Lesson 8-14”, Problem 1, students use a diagram to make sense of a word problem. “Javon and Sam are sharing a pizza. Javon eats 1-half of the pizza. Sam eats 1-fourth of the pizza. Draw and label the pizza to show how much each friend eats.” Students are given a picture of a circle. “If another friend joins them, name what part of the pizza she can eat. Use pictures, words, or both to show how you figured it out.”

Materials provide intentional development of MP2 to meet its full intent in connection to grade-level content. Students reason abstractly and quantitatively as they work with the support of the teacher and independently throughout the units. Examples include:

• Routine 3, Extending the Attendance Routine, students attend to the meaning of quantities when using a display of class attendance using a parts-and-total diagram. “When you introduce this diagram, ask children what numbers should go in each space in the diagram. Have the Attendance Helper explain which numbers represent the parts and the total each day.”

• Lesson 1-7, Organizing Data in a Tally Chart, Focus: Introducing Tally Marks, students represent situations symbolically when learning to use tally marks to create mathematical representations of numbers. “Have children draw tally marks on their slates to represent different numbers. Say to children: Show the number 10 using tally marks. The number 11. The number 18. As you call out a number, point to it on the Class Number Line or hold up the appropriate number card.”

• Lesson 6-4, Introducing Near Doubles, Focus: Developing the Near-Doubles Strategy, students demonstrate understanding of mathematical representations when shown two “Quick Look” cards for 2-3 seconds that have arrangements of dots. The first card is arranged as a doubles fact, the second shows dots arranged as that doubles fact plus one. “Ask children to share what they saw and how they saw it.”

• Independent Problem Solving 2b, “to be used after Lesson 2-11”, Problem 2, students create a word problem to represent an equation. “Write a number story to go with this equation. Solve. You may wish to draw a picture to help.” Students are given the equation “___ + 4 + 10.”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice). 

Materials provide support for the intentional development of MP3 by providing opportunities for students to construct viable arguments in connection to grade-level content. Examples include:

• Lesson 2-5, 10 Apples, Focus: Find the Missing Day, students construct viable arguments as they discuss strategies for determining whether any days of the week are missing from a journal page. “Are any days missing? Which days are missing? Tell your partner how you know.”

• Lesson 4-4, Measuring a Marker, Focus: Making Arguments, Math Journal 1, Problem 1, students construct viable arguments as they share strategies and discuss which ribbon they believe is longer. “Have children share their answers for Problem 1. Ask volunteers to explain how they decided which ribbon was longer. Sample answer: The top one looked longer. I could fit more paper clips along the top ribbon. I used a string to show how long one ribbon was, then lined the string up with the other ribbon.”

• Independent Problem Solving 4a, “to be used after Lesson 4-4”, Problem 2, students construct viable arguments about measurement tools. “Katelyn used a paperclip to measure the length of her journal. Now she wants to measure one side of the school building. Would using her paperclip make sense to measure one side of the school building? Why or why not?”

Materials provide support for the intentional development of MP3 by providing opportunities for students to critique the reasoning of others in connection to grade-level content. Examples include:

• Lesson 7-10, Addition Facts: “What’s My Rule?” Practice: Math Boxes, Problem 5, students critique the reasoning of others when analyzing the expression 3 + 4. “Raol wants to show (picture of 7 longs) in the box. Is that right or wrong? Explain. Sample answer: That’s wrong because that shows 7 tens and (picture of 7 cubes) is 7 ones.”

• Unit 9, Two-Digit Addition and Subtraction and Review, Open Response Assessment, students critique the reasoning of others as they analyze another student’s work in a number-grid. “Deena filled in the number-grid puzzle. Finish the puzzle and find her mistake. Cross out her mistake and write the correct number. Explain how you used patterns in the number grid to correct Deena’s mistake.”

• Independent Problem Solving 1a, “to be used after Lesson 1-5”, Problem 2, students critique an argument about the number of shoes being worn by classmates. “How many shoes are there in class today? How do you know? Yasi says she can count by 2s to find the number of shoes. Do you agree? Explain.”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice). 

Materials provide intentional development of MP4 to meet its full intent in connection to grade-level content. Students model with mathematics to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 2-11, Finding Unknowns, Focus: Modeling Unknowns, students model the situation with an appropriate representation as the teacher is encouraged to, “Remind children about their recent work with number models. Tell them that today they will write more number models to represent number stories. Jackie dropped 3 pennies in a cup. Then she dropped 4 more pennies in the cup. She dropped 7 pennies in all. Display a change-to-more diagram and have children help you complete it. Have children suggest a representative number model and record it.” 

• Independent Problem Solving 1b, “to be used after Lesson 1-10”, Problem 1, students model the situation as they write a number sentence to represent a picture. “Use the picture to write a number story.” Students are given a picture of a rack with 3 shelves containing various balls (basketballs, soccer balls, footballs, etc.). “Solve your number story. Use pictures or numbers to show your thinking.”

• Independent Problem Solving 8a, “to be used after Lesson 8-4”, Problem 2, students model the situation with an appropriate representation and use an appropriate strategy as they reason about shapes and their attributes. “a. Cole’s family is also sharing a pizza. Cole suggests cutting the pizza as shown below. Is this a fair way to share the pizza between the four people in Cole’s family? Use words and drawings to show your thinking. b. For dessert Cole’s family shares a giant brownie. Show two ways they could share the brownie fairly.”

Materials provide intentional development of MP5 to meet its full intent in connection to grade-level content. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 5-12, Adding Animal Weights, Focus: Solving the Open Response Problem, students choose appropriate tools and strategies as they solve an open-response problem. “Ask children to name some other tools they have used to add. Make a list of the tools on the board. Be sure number grids, number lines, and base-10 blocks are on the list. Tell children that they will choose one of the tools from the class list and use it to add animal weights.”

• Independent Problem Solving 6b, “to be used after Lesson 6-11”, Problem 1, students choose and use appropriate tools and strategies as they compare numbers using place value. “Use your toolkit coins, base-10 blocks, number grid, or another tool to help you. You want to buy a notebook that costs 70 cents. Find the total money in cents for each choice below. Draw an X on the choices that are not enough money to buy the notebook.”

• Independent Problem Solving 9b, “to be used after Lesson 9-8”, Problem 1, students choose appropriate tools and strategies as they compare weights. “Use your Animal Cards for these problems. Use base-10 blocks, a number grid, drawings, or another tool to help you. A pair of first-graders and a pair of animals are going to ride together in wagons. Circle the pair that weighs more. Two first-grade girls. A beaver and a koala. Write or show how you decided. Write a number model with < or > to compare the total weight of the pair of first-graders and the total weight of the pair of animals.”

The materials reviewed for Everyday Mathematics 4 Grade 1 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards. 

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice). 

Materials provide intentional development of MP7 to meet its full intent in connection to grade-level content. Students look for and make use of structure throughout the units as they describe, and make use of patterns within problem-solving as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 7-3, Relating Special Addition and Subtraction Facts, Focus: Think Addition to Subtract with Combinations of 10, students analyze a problem and look for more than one approach. “Point out that understanding combinations of 10 can also be useful for games such as Fishing for 10. For example, if they are holding a 3, they may think 3 + ___ = 10 or 10 - 3 = ___. Therefore, thinking of addition might help them solve problems involving decomposing a 10.” 

• Lesson 9-9, Review: Place Value, Focus: Making Up and Solving Number-Grid Puzzles, students look for patterns or structures when using place value understanding to create and solve number-grid puzzles. “Have children fold Math Masters, page TA43 into four equal parts. Invite children to make up number-grid puzzles that their partners can solve using their understanding of tens and ones patterns on the number grid. Children draw around some of the grid cells on one part of the sheet to make a puzzle piece and then write a 2-digit number in one of the cells. They trade puzzles with their partners who then fill in all of the missing numbers.”

• Independent Problem Solving 4b, “to be used after Lesson 4-10”, Problem 1, students look for and explain the structure within mathematical representations as they solve addition problems. “Think of an addition doubles fact about this picture of an alligator. Write the fact below. ___ + ___ = ___. Write a story to fit the doubles fact you wrote.”

Materials provide intentional development of MP8 to meet its full intent in connection to grade-level content. Students look for and express regularity in repeated reasoning throughout the units to make generalizations and build a deeper understanding of grade level math concepts as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 2-6, More Counting On to Add, Focus: Introducing High Roller, students describe and explain the “counting on” strategy and the “turn-around” rule in their own words. “High Roller makes use of counting on and the turn-around rule. Refer to the Strategy Wall and introduce High Roller as practice for both strategies (assuming counting on has already been listed). Have children restate the turn-around rule and counting on strategy in their own words. If counting on has not yet emerged, display two dot dice, one with 5, the other with 3, and ask children how to find the sum. Have them share the strategies, and highlight counting on (starting with 5 and counting on, 6, 7, 8) when it emerges. Have children practice counting on with a second pair of dice (showing 6 and 4).”

• Lesson 3-6, Counting to Add and Subtract, Focus: Introducing Addition on the Number Line, students notice repeated calculations and make generalizations/create shortcuts as they solve addition problems. “Next, ask children to draw hops on the third number line to solve 2+9. Select children to show counting on from 2 and counting on from 9. Discuss which strategy is more efficient. Help children generalize that counting on from the larger number, or 9, is faster because there are fewer numbers to count.” 

• Independent Problem Solving 7a, “to be used after Lesson 7-4”, Problem 2, students use repeated reasoning when they define attributes of rectangles. “Find and draw 2 different things that are not shaped like rectangles. What are they? Use what you know about rectangles to explain why your shapes are not rectangles.”