Estimation to add and subtract 2-digit number - math grade 2 - lesson 36

Learn (40 minutes)

Note to the Teacher: In today’s lesson, students practice estimating to find sums and differences. Yesterday in Reflect, students wrote their own addition and subtraction word problems. If possible, select some of those problems to use during today's lesson. Students always feel empowered when they see their work used as an example.

STUDENTS DO: Raise hands and share predictions about what it means to estimate.

TEACHER SAY: You made some great guesses. When we estimate, we think about the numbers in the problem and what numbers are close to those numbers and easier to work with. For example, let’s think about the number 18. Th at number can be hard to work with, so I am going to see if there is a number close to 18 that would be easier to work with.

TEACHER DO: Model looking at the 120 Chart to find a number close to 18.

TEACHER SAY: 20 is close to 18 and it is much easier to add and subtract than 18. It does not give me the exact right answer, but it helps me make a prediction about the answer. You help me do one. Think about the number 32. What number is close to 32 and is easier to add and subtract? Give me a Thumbs Up when you have an idea.

STUDENTS DO: Think about 32 and/or look at the 120 Chart. Give a Thumbs Up to volunteer. Selected students share their thinking.

TEACHER DO: Confirm students’ answers, if correct. Model looking at the 120 Chart to identify 30 as a number that is close to 32 and easier to work with or have students demonstrate how they did it.

TEACHER SAY: Let’s practice estimating with a fun game. I am going to make some estimates about answers to some math problems. If you think my estimate is a good guess, you will stand up. If you think my estimate is silly, make a silly face.

TEACHER DO: Post a few problems like the ones below on the board. Use students’ word problems from Reflect yesterday if possible. Do not write your estimate, but after you read each problem, share a silly estimate (examples below). Allow time for students to stand up or make a silly face. Ask one or two students to share why they think your estimate is close or silly after each problem. Examples:

• 16 + 20 = _____. My estimate is 94.

• This estimate is silly because if I look at the 120 Chart, I see that 16 is close to 20, so the answer to this problem would be much closer to 20 + 20, or 40. 90 is much too high.

• Reem made 27 beaded necklaces but her friends loved them so much, she made 32 more. How many beaded necklaces did she make all together? My estimate is 60.

• This estimate is close because 27 is close to 30 and 32 is close to 30. 30 + 30 is 60.

• 68 – 20 = ___. My estimate is 81.

• This estimate is silly because when we subtract, the difference will be less than the biggest number. This could be a good estimate for an addition problem, but it is a silly estimate for this subtraction problem.

2.TEACHER SAY: You did some great mathematical thinking about whether my estimates were close or silly. When we estimate, we can try a few strategies. We can use the 120 Chart strategy we used before. We can also use a place value strategy. When we use this strategy, we work only with the digits in the highest place value. Let’s try this strategy together.

TEACHER DO: Write at least two problems on the board like the examples below. Use students’ story problems from Lesson 35 Reflect, if possible. Use the following problem as an example, if needed (otherwise substitute the numbers below for the numbers in the problem you are using): Write 52 + 34 = ___ on the board.

TEACHER SAY: To use the place value strategy, first I circle the digits in the highest place value. In 2-digit numbers, the highest place is the Tens place, so I circle the 5 for 50 in the first number and 3 for 30 in the second number.

TEACHER DO: Circle the 5 in 50 and the 3 in 30.

TEACHER SAY: I also circle the addition sign because that tells me what to do with these numbers.

TEACHER DO: Circle the addition sign.

TEACHER SAY: I can use mental math to add 50 and 30. The answer is 80, so my estimate for the answer to 52 + 34 is 80. Let’s look at another example together. Ali bought 28 loaves of bread for his family. They ate 17 loaves. How many did they have left over? To use the place value strategy, first I will write this story problem with just numbers.

TEACHER DO: Write 28 – 17 = ___ on the board. Discuss the order of the numbers in the problem, if necessary.

TEACHER SAY: Now I circle the digits in the Tens place for each number, so I circle 2 for 20 and 1 for 10. I also circle the subtraction sign to remind me to subtract.

TEACHER DO: Circle the 2 in 28, the 1 in 17, and the subtraction sign.

TEACHER SAY: Now I can use mental math and figure out that 20 – 10 is 10, so I estimate the answer to 28 – 17 should be close to 10. What questions do you have about using the place value strategy to estimate?

STUDENTS DO: Ask questions about estimation, if necessary.

TEACHER DO: Answer students’ questions, if any.

TEACHER SAY: Turn to your Shoulder Partner and explain how to use place value to estimate.

STUDENTS DO: Talk to their Shoulder Partner about how to use place value to estimate.

TEACHER DO: Listen as students talk, supporting conversations as needed. Identify a few students to share their ideas.

TEACHER SAY: I will call on a few of you now to share what you and your Shoulder Partner discussed.

STUDENTS DO: Selected students share their explanations in their own words.

3.TEACHER SAY: You have got it. When we use the place value strategy for estimation, we simply add or subtract the digit in the highest place value. For us, that is the Tens place. That often gives us a good estimate of the answer. You and your Shoulder Partner will now get a chance to practice this together. Please open your student book to page Lesson 36: Apply.

STUDENTS DO: Open the student book to page Lesson 36: Apply.

TEACHER SAY: I want to remind you not to SOLVE these problems. You are going to circle three things: the digit in the Tens place in the first number, the digit in the Tens place in the second number, and the addition or subtraction sign. Then calculate your estimate. There are also two story problems on the page. Write the number sentence, circle the numbers in the Tens place, and calculate your estimate.

TEACHER DO: If necessary, read the story problems aloud to students.

STUDENTS DO: Take out the student book and work with a Shoulder Partner. Each student should complete the problems in their own book, but work with their Shoulder Partner for support if needed.

TEACHER DO: As students work, circulate around the room to answer any questions. Note which students may need additional instruction or support. Remind students to circle the digits and the sign and then estimate. If students are solving the problems, remind them to estimate. As Learn time comes to an end, use an Attention Getting Signal to bring the class back together.

3.TEACHER SAY: You and your partner worked really well together using the place value strategy for estimation. Let's go over our work together now. I will use the Calling Sticks for each problem to choose one student to share their estimate. If you estimated something different, please raise your hand.

STUDENTS DO: Selected students share their estimates.

TEACHER DO: If other students estimated something different, have them share their estimates. Discuss which estimate was more reasonable or ask the class to debate which one is more reasonable based on what they know about place value.