correctionkey=nl-a do not edit--changes must be made ......2-digit numbers, sometimes resulting in...

Dr. Karen C. Fuson, Math Expressions Author

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From Our Curriculum Research Project: 2-Digit Addition

In this unit, children will use physical objects, and then drawings, to demonstrate the concept of grouping ones into a new ten, or tens into a new hundred. From research, we see that children are able to readily comprehend the concept of new tens or new hundreds when they use models and make drawings.

Children are encouraged to develop their own methods of adding 2-digit numbers, before being given any instruction. Using models and drawings, children readily develop their own methods of adding. This unit concentrates on the addition of 2-digit numbers, with and without grouping. Children will generate their own techniques and learn other commonly-used methods.

From Current Research: Using Models to Represent Multidigit Addition

Research indicates that students’ experiences using physical models to represent hundreds, tens, and ones can be effective if the materials help them think about how to combine quantities and, eventually, how these processes connect with written procedures. . . . In order to support understanding, however, the physical models need to show tens to be collections of 10 ones and to show hundreds to be simultaneously 10 tens and 100 ones.

National Research Council: Developing Proficiency With Whole Numbers Adding It Up: Helping Children Learn Mathematics Washington, D.C.: National Academy Press, 2001. 198.

Research–Best Practices

Putting Research into Practice

Unit 2 | Overview | MB1-U2

DO NOT EDIT--Changes must be made through "File info" CorrectionKey=NL-A

Other Useful References: Addition

From Current Research: Advantages of Student Math Drawings

Student math drawings of problem situations and/or solution methods enable students to explain their thinking more clearly and explicitly by pointing to parts of their drawing as they explain, and enable listeners to understand because of the relating of language and visuals.

Students can relate parts of the drawing to the problem situation by labeling those parts. Students can relate in the drawing (e.g., by using an arrow) a step with quantity drawings (e.g., making 1 new ten from ten ones) to that same step in the numerical method (e.g., writing the new 1 ten in the tens column).

Math drawings are windows into the minds of students that allow teachers to understand student approaches and errors on homework and classwork. They enable teachers to do continual assessment for instruction. Teachers can always follow up on a math drawing by asking a student to explain it, but this frequently is not even necessary to understand student thinking.

Fuson, K., Atler, T., Roedel, S., Zaccariello, J. "Building a Nurturing Visual Math-Talk Teaching-Learning Community to Support Learning by English Language Learners and Students from Backgrounds of Poverty," New England Mathematics Journal, 41, 2009. 6

Research and Math Background

Number and Operations Standard for Grades Pre-K–2 Principles and Standards for School Mathematics. Reston, VA: National Council of Teachers of Mathematics, 2000. 79–87.

Carpenter, T.P., Franke, M.L., Jacobs, V.R., Fennema, E., & Empson, S.B. “A longitudinal study of invention and understanding in children’s multidigit addition and subtraction.” Journal for Research in Mathematics Education, 29, 1998. 3–20.

MB2-U2 | Unit 2 | Overview


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Getting Ready to Teach Unit 2

Learning Path in the Common Core StandardsIn this unit, children work with place value, representing numbers in different ways, and comparing numbers. They add two, three, or four 2-digit numbers, sometimes resulting in new tens or new hundreds, with sums to 200.

Visual models and real world situations are used throughout the unit to help children understand the value of 2- and 3-digit numbers and how to find the sum of 2-digit numbers.

Help Children Avoid Common ErrorsMath Expressions gives children opportunities to analyze and correct errors, explaining why the reasoning was flawed.

In this unit we use Puzzled Penguin to show typical errors that children make. Children enjoy teaching Puzzled Penguin the correct way, why this way is correct, and why Puzzled Penguin made the error. Common errors are presented in the Puzzled Penguin feature in the following lessons:

• Lesson 3: Miscounting the number of Quick Tens and ones in a math drawing

• Lesson 5: Starting with the digits in the ones place when comparing multidigit numbers

• Lesson 7: When using the Show All Totals Method to add 2-digit numbers, incorrectly lining up the tens total and the ones total

• Lesson 9: Forgetting to record the new ten when adding

• Lesson 10: Incorrectly recording tens and ones digits when adding

• Lesson 14: Recording the wrong number of new tens

In addition to Puzzled Penguin, there are other suggestions listed in the Teacher Edition to help you watch for situations that may lead to common errors. As a part of the Unit Test Teacher Edition pages, you will find a common error and prescription listed for each test item.

As you teach this unit, emphasize understanding of these terms.

• number flash• proof drawing

See the Teacher Glossary.

Math ExpressionsVOCABULARY



1 1 1 21 912 12 22 923 13 23 934 14 24 945 15 25 956 16 26 967 17 27 978 18 28 989 19 29 9910 20 30 40 50 60 70 80 90 100

101102103104105106107108109110

313233343536373839

414243444546474849

515253545556575859

616263646566676869

717273747576777879

818283848586878889

10

11

110

1 0

Math Background

Investigate Structure of the Base-Ten SystemLesson 1

This lesson lays the foundation for understanding the role of place value in the base-ten number system. Writing numbers, using layered place value cards, and making drawings help children connect quantities and numbers and understand the relationship of ones, tens, and hundreds.

Writing Numbers to 110 As children write the numbers from 1 to 110 in columns on their MathBoards, they continually see the grouping of ones to make tens and observe the patterns formed within the number sequence.

Model Tens and Ones The Secret Code Cards are research-based manipulatives for modeling numbers. In two-digit numbers, their purpose is to help children see the underlying structure of tens and ones. As children model numbers, they build understanding of place value concepts.

from the Progressions for the Common Core State Standards On Number and Operations In Base Ten

Understand Place Value In Grade 2,

students extend their understanding

of the base-ten system by viewing

10 tens as forming a new unit

called a “hundred.” This lays the

groundwork for understanding the

structure of the base-ten system

as based in repeated bundling in

groups of 10 and understanding

that the unit associated with each

place is 10 of the unit associated

with the place to its right.



5. In the lunchroom, 16 children have apples. Nine of these children have red apples and the rest have green apples. Then 5 more children come with green apples. How many children have green apples now?

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Drawing Numbers in Groups of 10 By using circles to represent ones and using lines to group the ones into tens, children reinforce place value concepts. They can name numbers as ones, as tens, or as hundreds. This work prepares them for using Quick Hundreds and Quick Tens to represent numbers in later lessons.

10 20 304050 60 70 8090 100

Problem Solving and Fluency Practice Throughout Unit 2, children will build fluency with addition and subtraction within 20 and will practice solving one- and two-step word problems for the addition and subtraction problem subtypes covered in Unit 1.

children12

apple



100

1 0 0 90

9 0 6

6

100

1 0 0 90

9 0 6

6 Hundreds Card Tens Card

Assembled Cards

Ones Card

196 = 100 + 90 + 6

Math Background

Represent NumbersLessons 2, 3, and 4

Different Ways to Represent Numbers By using math drawings, expanded form, Secret Code Cards, and numerals to represent numbers with hundreds, tens, and ones, children continually build understanding of place value. The examples below are for the number 196.

Math Drawings Quick Hundreds, Quick Tens, and circles are used to represent hundreds, tens, and ones. Notice that the math drawings are similar to base ten blocks. Using 5-groups within each place helps children see each number and be more accurate.

Expanded Form Children write an equation to show a number as the sum of the values of the digits in each place.

Secret Code Cards When children assemble these layered place value cards to represent the hundreds, tens, and ones in a number, they can see the place value of each digit in the small number printed on the top left corner of each card. When the cards are assembled, these numbers show the values of the expanded form of the number.

Numerals Children connect number names and numerals as they practice reading and writing numbers.

Addition of 1, 10, or 100 to a Number To prepare for 2-digit addition, children investigate patterns that occur when 1, 10, or 100 is added to a number, and begin to make these computations mentally.


Understand Place Value

Representations such as

manipulative materials, math

drawings, and layered three-digit

place value cards afford connections

between written three-digit

numbers and hundreds, tens, and

ones. Number words and numbers

written in base-ten numerals and

as sums of their base-ten units can

be connected with representations

in drawings and place value cards,

and by saying numbers aloud and in

terms of their base-ten units, e.g.,

456 is “Four hundred fifty-six” and

“four hundreds five tens six ones.”

one hundred ninety-six 196



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Understand place value Comparing

magnitudes of two-digit numbers

draws on the understanding that

1 ten is greater than any amount

of ones represented by a one-digit

number. Comparing magnitudes

of three-digit numbers draws on

the understanding that 1 hundred

(the smallest three-digit number)

is greater than any amount of tens

and ones represented by a two-digit

number. For this reason, three-digit

numbers are compared by first

inspecting the hundreds place.

Compare NumbersLesson 5

Children have used the symbols <, >, and = to show relationships between numbers up to 20. Now they will use them to show the results of comparing numbers with up to 3 digits. They will discuss and explore ways of comparing two numbers as they develop an efficient method for doing this.

Representations Comparing numbers symbolically may be difficult for children to do immediately, so using Math Drawings or Secret Code Cards to represent the numbers provides the needed support to help children build understanding. Children need to understand that the most efficient way to compare numbers is to start comparing the value of each place with the leftmost digit. Using the drawings or cards lets children see that by comparing the quantities in each place from left to right they can easily find the first (and so the greatest) place in which one number has a greater digit.

Because some children will have a tendency to start by comparing the ones digits first, guide them to see how that method can lead to making an error. For example, 20 > 15, even though 5 ones is more than 0 ones.

Place Value Working with Math Drawings or Secret Code Cards leads children to see that the most efficient way to compare numbers is to start at the leftmost digit, and that they can simply compare the value of the digit in each place moving from left to right. Some children may benefit from a transitional step in which they first write each number in expanded form and then compare the hundreds, the tens, and the ones, in that order.



Math Background

Two-Digit Addition MethodsLessons 6, 7, and 8

Explore Methods Children begin two-digit addition with situations that lead to an extra (or new) ten or an extra (or new) hundred. They use math drawings or other methods, some remembered from last year, to see how the new ten or new hundred is formed.

Show All Totals In this method, children find the total for each place and then add the place totals to find the total. Although work in this unit is limited to adding two 2-digit numbers, the method can be extended to as many places as desired.

In this unit, children carry out this method working from left to right, starting with the tens place; however, children may instead work from right to left, starting with the ones place.

New Groups Below As children add, they write the small 1 for a new ten at the bottom of the tens column. This method has two advantages: (1) writing the 1 below helps children see that the new ten came from the 10 ones in the teen number total of the ones column, and (2) the last addition in the column will always be + 1, which is easy to find, since the children will have added the other two (usually greater) digits first.

the added tens

the added ones

the hundreds, tens, and ones total

78 + 56

_

120 14

_

134

the new hundred

11

the new ten

78 + 56

_

134



100 + 30 + 4 = 134

Proof Drawings Just as mathematicians do, children should check their numerical work. To do this, children use math drawings as proof drawings. When they reconstruct the computation with a math drawing, if they find that the result is the same as the numerical computation, children can be sure that their work is correct.

However, using proof drawings has an even more important purpose. The proof drawings help make the steps of the numerical method meaningful to children. Guide children to explain how the parts of the proof drawing are connected to the parts of the numerical method. Children can use proof drawings for the two methods described and also for methods that they may generate themselves.

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Math Background

Compare Addition MethodsLessons 9 and 10

Because children learn and work in different ways, some children may be more comfortable with one method (either one they learned or one they generated themselves) than with the other methods. For example, some children may want to use Show All Totals working from right to left.

Discuss Methods As children discuss and solve the problems in these two lessons, they compare the methods, listen to advantages and disadvantages of the methods, and try different methods. This approach helps them decide which method they want to use.

It is important they understand that they do not have to choose and use only one method. Some children may decide that they want to use one method for one problem and a different one for a different problem, depending on the kinds of numbers in the problems.

One method may also lead children to understanding and using a different method. For example, children who work from right to left using Show All Totals may find with time that they are ready to use New Groups Below, because they now see how the total from the ones column may form a new ten for the tens column and that it is more efficient to write the small 1 at the bottom of the tens column than to write two separate totals.


Grade 2 Grade 2 students build

upon their work in Grade 1 in two

major ways. They represent and

solve situational problems of all

three types which involve addition

and subtraction within 100 rather

than within 20, and they represent

and solve two-step situational

problems of all three types.



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Understand Place Value Students

begin to work towards

multiplication when they skip

count by 5s, by 10s, and by 100s.

This skip counting is not yet true

multiplication because students

don’t keep track of the number of

groups they have counted.

Solve Word Problems Involving MoneyLessons 11 and 12

The Grade 2 Common Core State Standards for Measurement and Data ask that children solve word problems involving dollar bills, quarters, dimes, nickels, and pennies. These two lessons help meet that standard. Children will work with quarters in Unit 4.

Pennies, Dimes, and Dollars As children form amounts of money with pennies, dimes, and dollars, they see that these money units are related in the same way as ones, tens, and hundreds. They learn to use the dollar ($) and cent (¢) symbols, and are introduced to the decimal point notation for money amounts that use the dollar symbol.

Pennies, Nickels, and Dimes Children examine the relationship among these money units and find an efficient way to count money—starting with the coin with the greatest value. They practice skip counting as a way to count the coins, and learn to shift the amount of skip counting with each different coin.

Create and Solve Real World Problems A real world setting—the Farm Stand at Mr. and Mrs. Green’s grocery store—is the context in which children create and solve problems involving money amounts. Children select two kinds of produce and find the cost of purchasing both. This open-ended situation helps children discover that when two money amounts are both more than 50¢, the total of the two will be greater than $1.

Potatoes 65¢

Corn 56¢

Bananas 89¢

Peaches 77¢

Radishes 76¢

Lemons 88¢

Celery 57¢

Peppers 78¢



Math Background

Develop Addition Fluency and SkillsLessons 13 and 14

Children in Grade 2 are expected to fluently add within 100. This is important for satisfying the requirement of using addition and subtraction within 100 to solve one-step and two-step word problems. As children become more fluent in performing addition, they are better able to focus their attention on the meaning of a problem situation, to decide what situation type a problem involves, and to select a method for solving a problem.

Fluency for Addition Within 100 As children add two 2-digit numbers, they focus their attention on deciding whether a new 10 is formed during the addition. This helps them work more accurately and avoid errors.

More than Two Addends Children extend their addition skills to adding with 3 and 4 addends. They explore ways to do this and develop strategies for these additions.

Focus on Mathematical PracticesLesson 15

The Standards for Mathematical Practice are included in every lesson of this unit. However, the last lesson in every unit focuses on all eight Mathematical Practices. In this lesson, students apply what they have learned about making sense of problems, modeling, and reasoning to what they have learned about adding two-digit numbers in order to solve problems about recycling.


Grade 2 The word fluent is used

in the Standards to mean “fast

and accurate.” Fluency in each

grade involves a mixture of just

knowing some answers, knowing

some answers from patterns

(e.g., “adding 0 yields the same

number”), and knowing some

answers from the use of strategies.

It is important to push sensitively

and encouragingly toward fluency

of the designated numbers at

each grade level, recognizing that

fluency will be a mixture of these

kinds of thinking which may differ

across students.



Add with New Groups Below MP1 Make Sense of Problems | Analyze the Problem Have children work in pairs to complete Student Activity Book pages 107–108. Before each exercise, have partners predict whether adding the numbers together will make a new hundred, a new ten, both, or neither. Pairs should discuss their predictions and check after adding to see if each prediction was correct.

from Lesson 2-8

MP1 Make Sense of Problems | Use a Different Method Write these number comparisons on the board, and have children copy them on their MathBoards:

63 27

118 142

99 105

Invite pairs of children to complete each statement, with each partner representing the numbers in a different way. The first child uses drawings, and the second child uses Secret Code Cards.

from Lesson 2-5

Mathematical Practices

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Using the Common Core Standards for Mathematical PracticesThe Common Core State Standards for Mathematical Content indicate what concepts, skills, and problem solving children should learn. The Common Core State Standards for Mathematical Practice indicate how children should demonstrate understanding. These Mathematical Practices are embedded directly into the Student and Teacher Editions for each unit in Math Expressions. As you use the teaching suggestions, you will automatically implement a teaching style that encourages children to demonstrate a thorough understanding of concepts, skills, and problems. In this program, Math Talk suggestions are a vehicle used to encourage discussion that supports all eight Mathematical Practices. See examples in Mathematical Practice 6.

Mathematical Practice 1Make sense of problems and persevere in solving them.

Children analyze and make conjectures about how to solve a problem.They plan, monitor, and check their solutions. They determine if their answers are reasonable and can justify their reasoning.

Unit

2

Make Sense of ProblemsAnalyze RelationshipsDescribe Relationships

Look for a PatternUse a Different MethodAnalyze the Problem

Act It OutDraw a Diagram

Teacher Edition: Examples from Unit 2

Mathematical Practice 1 is integrated into Unit 2 in the following ways:

Unit 2 | Mathematical Practices | MB13-U2



Show All Totals Method MP2 Reason Abstractly and Quantitatively | Connect Symbols and Words Read aloud Problem 1 on Student Activity Book page 105. Write the addends in vertical form on the board and direct children to do the same on their MathBoards. Tell children that they will now learn how Mr. Green uses the Show All Totals method to solve the problem.

25 + 48

_

Children explored this method in Grade 1. Ask a volunteer who remembers this method to demonstrate how to work through the steps. That child can work at the board as the rest of the children work on their MathBoards.

from Lesson 2-7

MP2 Reason Abstractly and Quantitatively | Connect Symbols and Models Write the following amounts on the board: 165¢, 178¢, 157¢. Allow groups of children to represent each amount by drawing dollars, dimes, and pennies on their MathBoards. After representing each amount with a drawing, children should record that amount using a dollar symbol and a decimal point.

from Lesson 2-11


Mathematical Practice 2Reason abstractly and quantitatively.

Children make sense of quantities and their relationships in problem situations. They can connect diagrams and equations for a given situation. Quantitative reasoning entails attending to the meaning of quantities. In this unit, this involves place value understanding to 200 and addition within 200.

Reason Abstractly and Quantitatively

Connect Symbols and Words Connect Symbols and Models Connect Diagrams and Equations

MB14-U2 | Unit 2 | Mathematical Practices


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Is the Statement True? Write the following on the board.

A bag holds 4 nickels, 4 pennies, and 4 dimes. If 3 coins are taken out of the bag, the value of the 3 coins can never be more than 16 cents.

Children decide if the statement is true or false, and use words and models to support their position. The statement is false.

MP3 Construct a Viable Argument | Justify Conclusions Children should be able to explain whether they think the statement is true or false and how they know they are correct.

from Lesson 2-15

MP3, MP6 Construct Viable Arguments/Critique Reasoning of Others | Puzzled Penguin Copy the addition example as shown below on the board.

• Puzzled Penguin wrote this addition exercise and says that this is one way to find the sum of the four addends.

• What was Puzzled Penguin’s mistake? Puzzled Penguin did not record the new tens correctly. 4 + 7 + 9 + 6 = 26, which has 2 tens. Puzzled Penguin only recorded 1 new ten. Does everyone agree? yes

from Lesson 2-14


Mathematical Practice 3Construct viable arguments and critique the reasoning of others.

Children use stated assumptions, definitions, and previously established results in constructing arguments. They are able to analyze situations and can recognize and use counterexamples. They justify their conclusions, communicate them to others, and respond to the arguments of others.

Children are also able to distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Children can listen to or read the arguments of others, decide whether they make sense, and ask useful questions to clarify or improve the arguments.

MathTalk is a conversation tool by which children formulate ideas and analyze responses, and engage in discourse. See also MP.6 Attend to Precision.

24 1 7

29 + 26

_

86

1

Construct Viable ArgumentsCritique the Reasoning of Others

Compare Methods Puzzled PenguinJustify Conclusions



MP4 Model with Mathematics | Draw a Model Direct children’s attention to Student Activity Book page 120. On this page, children will be determining the values of groups of nickels. Point out to children that in the first three exercises on the page, the coins are pictured for them. For the last problem, they will need to draw the nickels. Demonstrate how to represent a nickel by drawing a circle with a 5 written inside.

from Lesson 2-12

MP1, MP4 Make Sense of Problems/Model with Mathematics | Draw a Diagram Read aloud Problem 1 on Student Activity Book page 103. Have a few volunteers represent the numbers 56 and 28 with sticks and circles on the board as the rest of the class work at their seats.

Have children write the problem in numbers on the board. Be sure they show both the horizontal and vertical formats.

from Lesson 2-6


Model with MathematicsDraw a Diagram

Make a ModelDraw a Model

Write an Equation


Mathematical Practice 4Model with mathematics.

Children can apply the mathematics they know to solve problems that arise in everyday life. This might be as simple as writing an equation to solve a problem. Children might draw diagrams to lead them to a solution for a problem.

Children apply what they know, and are comfortable making assumptions and approximations to simplify a complicated situation. They are able to identify important quantities in a practical situation and represent their relationships using such tools as diagrams, tables, graphs, and formulas.



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MP5 Use Appropriate Tools | Secret Code Cards Student Activity Book pages 125–126 feature the directions for an activity that children can use to build fluency for addition within 100. Attach Demonstration Secret Code Cards to the board and invite two children to come to the front of the class to help you demonstrate how to do the activity. The focus of this activity is on deciding whether or not a new ten needs to be made.

from Lesson 2-13

MP5 Use Appropriate Tools | MathBoard Modeling Children should place their MathBoards with the Number Path facing them or use the Number Path (TRB M34).

• How many tens and ones are in the number 24? 2 tens and 4 ones

• How can we show 24 on the Number Path? We draw Quick Tens through the first 20 squares to show the two groups of 10. Then we draw circles on the next four squares to show the 4 ones.

from Lesson 2-2


Use Appropriate ToolsMathBoard

Secret Code CardsMathBoard Modeling

Use Gestures120 Poster


Mathematical Practice 5Use appropriate tools strategically.

Children consider the available tools and models when solving mathematical problems. Children make sound decisions about when each of these tools might be helpful. These tools might include paper and pencil, a straightedge, a ruler, or the MathBoard. Children recognize both the insight to be gained from using the tool and the tool’s limitations. When making mathematical models, they are able to identify quantities in a practical situation and represent relationships using modeling tools such as diagrams, grid paper, tables, graphs, and equations.

Modeling numbers in problems and in computations is a central focus in Math Expressions lessons. Children learn and develop models to solve numerical problems and to model problem situations. Children continually use both kinds of modeling throughout the program.

Equation

sticks and circlesto show 24



Mathematical Practice 6Attend to precision.

Children try to communicate precisely to others. They try to use clear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. They are careful about specifying units of measure to clarify the correspondence with quantities in a problem. They calculate accurately and efficiently, and express numerical answers with a degree of precision appropriate for the problem context. Children give carefully formulated explanations to each other.


Attend to PrecisionDescribe Methods

Puzzled Penguin

MathTalk in Action

Here is a sample classroom discussion that shows different ways children added 39 + 97.

Kate: I used the Show All Totals method.

39 + 97

_

120 + 16

_

136

Will: I used the New Groups Below method.

39+ 97

1361 1

James: I used the New Groups Below method.

136

1 139

+ 97

from Lesson 2-9

MP6 Attend to Precision Ask children where 38 is on this board. Be aware that some children may say that just the last square is 38. Make sure that children understand that the number 38 really means 38 things—all the squares on the Number Path up to and including that square make the quantity 38.

To show that 38 is all the squares, draw a loop around the 38 squares and write 38 near the last square you counted. Demonstrate this on a child’s board.

from Lesson 2-3




Write the Numbers 101 to 200 MP7 Look for Structure Have children erase the last column (the numbers 101–110) from their 10 × 10 grids on their MathBoards. Then have them place their MathBoards (showing 1–100) to the left of Student Activity Book page 87. Have them begin to fill in the table on the page. As children fill in the table, ask about patterns they see. Children should notice that as they fill in the boxes in each column from top to bottom, the digit in the ones place increases by one. They should also see that when they “read“ a row from left to right, the digit in the tens place increases by one. They may also discover that when they look at a top left to bottom right diagonal path, the digits in both the tens and ones places increase by one. If no child comments on it, point out the bottom row of numbers and ask children what pattern they see there. The tens digit increases by one each time, and the hundreds and ones digits stay the same. The last number in the row does not follow this pattern. Children should display understanding that these numbers are 11 tens, 12 tens, and so on; and that the last number represents 20 tens, which is equal to 200.

from Lesson 2-11

MP7 Look for Structure | Identify Relationships Elicit from children how the numbers in these exercises will change when 10 is added. Children should note that the value shown in the tens place increases by 1 ten.

• How are these exercises the same as the exercises where we added 1? How are they different? We increased by 1 in both kinds of exercises. When we added 1, we increased the number by 1 one. When we add 10, we increase the number by 1 ten.

• Look at 96 + 10. What happened when you increased 96 by 1 ten? We added 1 ten to 9 tens (and 6 ones). 9 tens + 1 ten = 10 tens. 10 tens is the same as 1 hundred; we had 1 hundred, 0 tens, 6 ones. 100 + 0 + 6 = 106.

Add 10 MathTalk

Write the following addition exercises on the board:

46 + 10 60 + 10 96 + 10

105 + 10 115 + 10

from Lesson 2-4

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Mathematical Practice 7Look for structure.

Children analyze problems to discern a pattern or structure. They draw conclusions about the structure of the relationships they have identified.

Look for Structure Identify Relationships Use Structure



MP8 Use Repeated Reasoning | Generalize

• Why did you compare the hundreds first? The hundreds have the greatest value in these numbers. If one number has more hundreds than the other number, I know that number is greater.

• What do you do if the numbers you are comparing have the same number of hundreds? If the number of hundreds is the same, I look at the next greatest place value position, which is the tens place.

from Lesson 2-5

Use Repeated Reasoning Identify Relationships Generalize


Identify a Pattern Draw the pattern sequence below on the board.

MP8 Use Repeated Reasoning | Generalize

• What number should we place under the 74? 95 Why?

from Lesson 2-15


Mathematical Practice 8Look for and express regularity in repeated reasoning.

Children use repeated reasoning as they analyze patterns, relationships, and calculations to generalize methods, rules, and shortcuts. As they work to solve a problem, children maintain oversight of the process while attending to the details. They continually evaluate the reasonableness of their intermediate results.

Student Activity Book: Lesson 15 Pages 129–130FOCUS on Mathematical PracticesUnit 2 includes a special lesson that involves solving real world problems and incorporates all 8 Mathematical Practices. In this lesson, children use what they know about adding, comparing numbers, and money to solve problems about recycling. Collected So Far

102 water bottles

88 pie plates

63 paper towel rolls

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Unit 2 • Lesson 15

Solve Problems and Compare MethodsTo recycle means to use again. The second graders at Center School are collecting trash. They will recycle the trash to make musical instruments.

Solve each word problem.1 Forty-eight children each want to make a pie

plate tambourine. Each tambourine is made with 2 pie plates. Do they have enough pie plates?

Circle yes or no. yes no

2 If the children collect 10 more water bottles, how many water bottles will they have?

label

3 If the children collect 29 more paper towel rolls, will they have enough to make 75 kazoos?

Circle yes or no. yes no

Paper Towel Roll Kazoo

Pie Plate Tambourine

Water Bottle Maracas

Name

water bottles112

Focus on Mathematical Practices 129 CC SS

Content Standards 2.OA.A.1, 2.NBT.A.2, 2.NBT.A.4, 2.NBT.B.5,2.NBT.B.7, 2.MD.C.8 Mathematical Practices MP1, MP4, MP5, MP6

DO NOT EDIT--Changes must be made through “File info”CorrectionKey=NL-A

2_MNLESE919747_U02L15.indd 129 12/9/16 8:54 AM

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Unit 2 • Lesson 15

Money for Cans and BottlesSome states help people recycle by giving money back when they return a bottle or can. This fleece jacket, this yo-yo, and this park bench are all made from recycled plastic bottles.

Solve each word problem.4 Suzanne and Jing get 5 cents for each can or

bottle they return. Suzanne returns 29 cans and 18 bottles. Jing returns 15 cans and 34 bottles. Who gets more money back?

5 Malia returns 12 bottles. She gets one nickel for each bottle. How much money does she get?

6 Roberto gets 5 cents for every can he returns. He gets $1.20. How many cans does he return?

label

cans24

$ 0.60 or 60¢

Jing

130 UNIT 2 LESSON 15 Focus on Mathematical Practices

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2_MNLESE919747_U02L15.indd 130 12/1/16 1:31 AM

34 44 54 64 74 8455 65 75 85 95 105



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