4.4 Using Tape Diagrams to Add and Subtract Multiples of 10

4.4 Using Tape Diagrams to Add and Subtract Multiples of 10

4.4 Using Tape Diagrams to Add and Subtract Multiples of 10

COMMON CORE STATE STANDARDS
Represent and solve problems involving addition and subtraction
2.OA.A.1 – Operations and Algebraic Thinking
Use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.1
1 Explanations may be supported by drawings or objects.
Use place value understanding and properties of operations to add and subtract
2.NBT.B.5 – Number and Operations in Base Ten
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
2.NBT.B.8 – Number and Operations in Base Ten
Mentally add 10 or 100 to a given number 100–900, and mentally subtract 10 or 100 from a given number 100–900.
2.NBT.B.9 – Number and Operations in Base Ten
Explain why addition and subtraction strategies work, using place value and the properties of operations.
BIG IDEA
Students will add and subtract multiples of 10 and some ones within 100 using tape diagrams.
Standards of Mathematical Practice
Make sense of problems and persevere in solving them
Reason abstractly and quantitatively
Construct viable arguments and critique the reasoning of others
Model with mathematics
□Use appropriate tools strategically
Attend to precision
□Look for and make use of structure
□Look for and express regularity in repeated reasoning / Informal Assessments
Math journal
□Cruising clipboard
□Foldable
□Checklist
Exit ticket
Response Boards
Problem Set
Class Discussion
PREPARING FOR THE ACTIVITY / MATERIALS
  • You will need linking cubes of three different colors and enough linking cubes of various colors for students to use as needed to support their work during the Problem Set.
/
  • Math Journals
  • Response boards
  • Dry erase markers
  • Linking Cubes
  • Problem Set 4.4
  • Exit ticket 4.4
  • Additional Practice 4.4

VOCABULARY
  • Benchmark number

AUTOMATICITY / TEACHER NOTES
Place Value
  1. Write 174 on the board and ask students to say the number (174).
  2. What digit is in the tens place? (7) Underline the digit 7 and ask for its value (70).
  3. What’s the value of the 1? (100). What’s the place of the 4? (Ones place)
  4. Erase the number and repeat for the following possible sequence: 258, 734, 860, and 902.
Making the Next 10 to Add
  1. Write 9 + 4 on the board. How can I make a ten? (Make it 10 + 3 because you can make a number bond with 4 and turn it into 1 and 3) Demonstrate on the board as follows:

  1. Ask students for the answer (13).
  2. Continue with the following possible sequences: 19 + 4, 29 + 4, 49 + 4, 79 + 4, 9 + 6, 19 + 6, 29 + 6, 59 + 6, 8 + 3, 18 + 3, 48 + 3, 8 + 5, 18 + 5, 88 + 5, 7 + 6, 17 + 6, 27 + 6, 7 + 4, 17 + 4, and 67 + 4.
/ Select appropriate activities depending on the time allotted for automaticity.
Place Value: Reviewing and practicing place value skills in isolation will prepare students for success with adding and subtracting tens and ones in the lesson.
Making the Next 10 to Add: This fluency will review foundations that lead into today’s lesson.
SETTING THE STAGE / TEACHER NOTES
Application Problem
1.Post the following problem on the board for students and read aloud:
Carlos bought 61 t-shirts. He gave 29 of them to his friends. How many t-shirts does Carlos have left?
2.Review the RDW procedure for problem solving: Read the problem, draw and label, write a number sentence, and write a word sentence. The more students participate in reasoning through problems with a systematic approach, the more they internalize those behaviors and thought processes.
3.Allow time for students to complete independently in their math journals. Circulate around the room and take note of students’ various strategies. Then, tell them to that they will go over the problem later in the lesson today.
Possible solution:

Connection to Big Idea
Today, we will continue adding and subtractingmultiples of 10 and some ones. / Note: This Application Problem is intended to come after the Explore the Concept so that students can apply what they have learned about making easy numbers (i.e., a multiple of 10) to subtract. You may choose to lead students through the RDW process or have students work independently and then share their work.
EXPLORE THE CONCEPT / TEACHER NOTES
  1. Show one row of 8 linking cubes made up of 5 in (yellow) and 3 in (red) and one row of 5 linking cubes made up of 5 (yellow) cubes.

  1. There are 5 yellow cubes in this stick. How many linking cubes are in this stick? Hold up the stick of 8 (8). What is the difference between 8 and 5? Break off the 3 red cubes that represent the difference (3). What number sentence could we use to represent the difference between 8 and 5? (8 – 5 = 3)
  2. Replace the red cubes on the stick and add one green cube to each stick and ask students if the difference changed (No because the sticks are still the same size and I can see the 3 red cubes).

  1. But what new number sentence can I use to represent the difference between my two sticks now?(9 – 6 = 3). Like you said the difference is still 3!
  2. Draw a two-bar tape diagram to represent the two sets of cubes you started with.

  1. I first started with these two sticks and then I added one more to each bar.Model as shown below:

Did the difference change?(No)Let’s test this idea out: When we add the same amount to each number in a subtraction sentence, the difference stays the same.
  1. Let’s try this with a new problem. Write 34 – 28 = ___ on the board. Now this is challenging but what about this one. Write 36 – 30 = ___ and ask students for the answer (6). How did you know the answer so fast? (Just take away 3 tens; Because 3 tens – 3 tens = 0 tens so you know you only have 6 ones left) Yes! It’s just way easier to subtract tens!
  2. Draw a tape diagram on the board to represent 34 – 28 without filling in the numbers. Direct students to do the same on their response boards. Call a student volunteer forward to label the tape diagram.

  1. Now, can you tell me how 34 – 28 and my other problem, 36 – 30, are related? Turn and talk (I think 34 – 28 is the same as 36 – 30 but she added two more to each number, so the difference must be the same).
  2. After sharing out, call a volunteer to add two to each bar on the board to change the model to 36 – 30. Students do the same at their seats.

  1. Now how long is each bar?(The bottom bar is 36, and the top bar is 30)We added 2 to each bar to make the problem easier!
  2. Now it’s your turn. On your response board, solve these problems by making a tape diagram. Add on to both numbers to make the problem easier.Write on the board: 22 – 8, 26 – 19, 33 – 18. If needed, guide the students in each of the problems if they have yet to grasp the concept.
  3. Show the following with the cubes:

There are 6 red cubes on one end and 4 red on the other end. How many yellows are in the middle? (1)What’s the total number of cubes? (11)
  1. Let’s make 2 different addition sentences. I’m going to join the 1 yellow cube with the 4 red:

What is the addition sentence for the total number of cubes? (6 + 5 = 11)
  1. Now, what if I join the 1 yellow with the 6 red instead?

What is the addition sentence now?(7 + 4 = 11)
  1. Write 6 + 5 = 7 + 4 on the board. How do you know this is true? (Both equal eleven; It’s just the 1 moved from one number to the other number; You can see that the number of cubes didn’t change) Draw the model below on the board to reinforce:

  1. Let’s use that same idea with larger numbers to make tens. Let’s solve 28 + 36.Draw a bar and label it 28. What does 28 need to be the next ten or benchmark number?(2)
  2. Add another chunk of 2 on to the right end of the bar of 28. What is 2 less than 36?(34) Draw the second bar to show the 34.

  1. Tell me why I drew 34 instead of 36. Turn and talk to a neighbor first (Because you used 2 from the 36 to make 28 into 30; Because it’s easy to add tens so we put 2 more on 28 to have 3 tens)Demonstrate on the board:


  1. How do you know this is true: 28 + 36 = 30 + 34? (You can see on the model; The two can go with the 28 or the 34; It was easy to make 28 to 30 because it is closer to the next ten).
  2. We can also show 2 more for 28 with a number bond.Write the number bond pictured below, working interactively with students as you see best for your class.

  1. Have students write both models in their math journals and explain them to a partner before providing more guided practice problems such as the following: 19 + 35, 36 + 29, 78 + 24, and 37 + 46.
  2. Tell students to take out their math journals to revisit the application problem from earlier. Ask students now that they have used the tape diagrams as another simplifying strategy, if they would like to make any changes to their work. Allow time for students to rework their problem if they would like to. Circulate the room, taking note of those students who may change what they have done to what they learned in today’s lesson.
  3. Have students turn and talk to discuss any changes they made. Then, choose several students to share out their strategies (see Teacher Notes for example).
Problem Set
Distribute Problem Set 4.4. Students should do their personal best to complete the problem set in groups, with partners, or individually. For some classes, it may be appropriate to modify the assignment by specifying which problems they work on first. Some problems do not specify a method for solving. Students solve these problems using the RDW approach used for the Application Problem. / Note: Guide students carefully in understanding what they see in the cubes into related number sentences.
UDL – Notes on Multiple Means of Representation:
  • Use a ruler to remind students that the length of an object, for example, a pencil, remains the same regardless of where it starts on the ruler.
  • You can, also, use a number line to show that age differences don’t change when people age. For example, Mark and Robert are 8 and 6 years old now. How old will they be in 3 years? What will be the difference in their ages?
UDL – Notes on Multiple Means of Engagement: Students with dysgraphia may benefit from using the model drawing tools on thinkingblocks.com.
Before circulating, consider reviewing the reflection questions that are relevant to today’s problem set.
REFLECTION / TEACHER NOTES
1.Invite students to review their solutions for the Problem Set. They should check their work by comparing answers with a partner before going over answers as a class.
2.Guide students in a conversation to debrief the Problem Set and process the lesson. You may choose to use any combination of the questions below to lead the discussion.
  • How did you label your tape diagram in Problem 1(b)? Why?
  • Share your tape diagram for Problem 2(b) with a partner. How did you label it to add tens?
  • Look at Problem 2(c): 61 + 29 = 60 + 30. Is this true? How do you know?
  • What other special strategy could you use to solve Parts (a–d) of Problem 1? How could you use the arrow way to solve these problems?
  • What do you notice about the numbers in the Problem Set today? When is the best time to use the tape diagram to solve?
  • What is the goal in using the tape diagram as a simplifying strategy?
  • Review the types of simplifying strategies students have done in the last few days and create a strategy chart with them to post in the room.
3.Allow students to complete Exit Ticket 4.4 independently. / Look for misconceptions or misunderstandings that can be addressed in the reflection.

Source:

Grade 2Units 4: Block 4

Name: ______Date: ______

Problem Set 4.4 – page 1

  1. Draw and label a tape diagram to help you subtract tens. Write the new number sentence and solve. The first one has been done for you.
  1. 23 - 9 = 24 – 10 = ___14__

+1 / 23
+1 / 9
  1. 32 – 19 = ______= ______

32
19
  1. 50 – 29 = ______= ______
  1. 47 – 28= ______= ______

Problem Set 4.4 – page 2

1. Draw and label a tape diagram or use a number bond to help you add tens. Write the new number sentence and solve.

a. 29 + 46 = __30 + 45__ = __75__

29 / 1 / 45

b. 38 + 45 = ______= ______

c. 61 + 29 = ______= ______

d. 27 + 68 = ______= ______

Name: ______Date: ______

Exit Ticket4.4

  1. Solve using a tape diagram or number bond.

a. 26 + 38 = ______= ______

b. 83 – 46 = ______= ______

2. Craig checked out 28 books at the library. He read and returned some books. He still has 19 books checked out. How many books did Craig return? Draw a tape diagram to help you solve.

Name: ______Date: ______

Additional Practice 4.4 – page 1

  1. Solve by drawing or completing a tape diagram to subtract 10, 20, 30, 40, etc.
  1. 17– 9 = 18–10 = ______
  1. 33 – 19
  1. 60 – 29
  1. 56 – 38

Additional Practice 4.4 – page 2

  1. Solve by drawing a number bond to add 10, 20, 30, 40, etc.
  1. 28 + 43 = 30 + 41 = _____

/\

2 41

  1. 49 + 26 = ______= _____
  1. 43+19 = ______= _____
  1. 67+28 = ______= ______
  1. Use a number bond or tape diagram to solve. Write your answer in a complete sentence.

Kylie has 28 more oranges than Cynthia. Kylie has 63 oranges. How many oranges does Cynthia have?

Top View