Guided Lessons

# Comparing Strategies for Three-Digit Addition

This lesson helps students develop an ability to compare and contrast as they explore two strategies to solve three-digit addition problems. This EL maths lesson can be used alone or alongside Three-Digit Addition Strategies Review.
This lesson can be used as a pre-lesson for theThree-Digit Addition Strategies ReviewLesson plan.

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This lesson can be used as a pre-lesson for theThree-Digit Addition Strategies ReviewLesson plan.

Students will be able to solve three-digit addition problems using various visual and written strategies.

##### Language

Students will be able to compare and contrast two methods for solving three-digit addition problems using base-ten blocks and sentence frames for support.

(4 minutes)
• Explain to the students that you are planning a very large dinner at a local community centre. Say, "I've been collecting names of people that want to come to the dinner. I've already collected 135 names of people who want to come. My friend collected 102 names of people who want to come to the dinner. I need to plan how much food I need to buy, but I'm not really sure where to start. Turn and talk to a partner, sharing your idea."
• Provide sentence stems to support students in discussing their ideas, such as:
• I think you should add the numbers because ____.
• I think you should subtract the numbers because ____.
• Allow a few students to share their ideas aloud. Confirm that adding the two numbers is the correct answer because you want to figure out how many people are coming to the dinner in all. Elaborate that since we are combining the two numbers, this means we need to add them together.
• Tell the students that today they will compare and contrast two StrategiesTo add three-digit numbers. Ask students to put their mathematician hats on!
(10 minutes)
• Pass out the Vocabulary Cards to each student and read through the student-friendly definitions. Show the students the visuals on the vocabulary cards and explain what they show to deepen student understanding. Clarify any confusion as needed.
• Write the following problem on the board: 135 + 102 = ____.
• Explain to the students that there are many ways we can solve this addition problem. Say, "We could start at 135 and count up by ones (e.g. 135, 136, 137). Turn and talk to your partner, explaining if that would be a good strategy to use."
• Provide sentence stems to support students in their discussions, such as:
• Counting by ones would be a good strategy to use because ____.
• Counting by ones would not be a good strategy to use because ____.
• Explain to the students that counting by ones would take a pretty long time. Tell the students that today you will solve the addition problem using two strategies.
• Tell the students that the first strategy involves using Base-ten blocksTo solve the problem.
• Take out base-ten blocks (or create sketches of base-ten blocks, such as a large square for one hundred, a long rectangle for ten, and a small square for one).
• Explain the representations of the base-ten blocks using Place valueTo support student understanding. Provide students with whiteboards and whiteboard markers and sets of base-ten blocks to use.
• Write a three-digit number on the board, such as 241. Show the students how to represent the chosen number using base-ten blocks. Next, ask students to work in pairs to create the number for you using their base-ten blocks.
• Write another number on the board. Ask students to work with an elbow partner to represent the number using base-ten blocks. Look around the room to check for understanding.
• Write a three-digit addition problem on the board and model how to solve the problem using base-ten blocks. Say, "I want you to think about this strategy. Does using base-ten blocks to solve three-digit addition problems make sense to you? I want you to turn and talk an elbow partner and explain why or why not." Provide students with the following sentence stems to support them in their discussions:
• Using base-ten blocks makes sense to me because ____.
• Using base-ten blocks doesn't make sense to me because ____.
• Explain to the students that now you will solve the same problem using the Standard algorithm. Explicitly solve the problem for students. When you are finished, have the students solve the same problem using a whiteboard and whiteboard markers with the same elbow partner. Ask students to hold up their whiteboard when they are finished and check for understanding.
(12 minutes)
• Show students the Strategy Cards: Three-Digit Addition cards. Tell the students that first they will match the base-ten block strategy cards to the corresponding card that shows the same problem represented using a standard algorithm. Explain to the students that after they finish matching the cards, they will compare and contrast the addition strategies.
• Elaborate that when you Compare, you think about how things are the same. When you Contrast, you think about how things are different. Provide an example by orally comparing and contrasting two common objects in the classroom (e.g. a pen and a marker). Write down some of your findings on the whiteboard.
• Put students in partnerships and ask them to sit somewhere comfortable in the classroom (this is a perfect opportunity for some floor time).
• Hand out a bag of the pre-cut Strategy Cards to each pair. Have students work together in partners to match the base-ten block strategy cards to the corresponding card that shows the same problem represented using a standard algorithm.
• Have partners use the the following sentence frame to compare and contrast the strategies together:
• The strategies are similar because ____.
• The strategies are different because ____.
• After working together with a partner to compare and contrast strategies, have each pair of students get together with another pair to share what they learned. Have them use one of the following sentence frames to guide their discussion:
• What our group noticed is that both strategies ____.
• What are group noticed is that one strategy ____.
• Support students to answer the questions by reminding them of the sentence frames they can use.
• Rotate around the classroom and listen to student discussions. Jot down important terms, ideas, and speaking and listening goals that are being met and opportunities for continued growth.
(10 minutes)
• Tell students that they are going to use what they have learned about different addition strategies to solve a problem. Share the following problem orally and write it on the board: "For the community dinner, my friend bought 150 chocolate candies to give out for dessert. I already had 120 chocolate candies. We know that 237 people are coming to our dinner. Will we have enough candies for everyone?"
• Have students turn to a partner and share how they might solve this problem. Hand out an index card to each student and have them write the number sentence they would use to solve the problem. Clarify that addition will be used to solve the problem because we are trying to figure out how much we have total when we combine 150 with 120.
• Tell one partner to solve the problem using the standard algorithm and one partner to solve the problem using base-ten blocks. Encourage students to refer to their vocabulary cards for support. Ask students to write their solutions on their index cards and show as much of their work as possible. Have the students who solve the problem using base-ten blocks keep their base-ten blocks out to represent the problem.
• Have students share their work with each other, explaining how they solved the problem.
• Then have students explain their partner's strategy back to them. This gives students an opportunity to make sure they understand their partner's reasoning while practising their language skills.
• Ask students to compare and contrast the strategies that were used by thinking about what is similar and what is different.
• Listen as students compare and contrast, providing them with support and sentence frames as needed. Consider rephrasing what students say so that they can have the opportunity to hear and revise their explanations.

Beginning

• Show the students an image of a community centre.
• Allow students to work with a partner who speaks the same home language (L1), if possible. If not possible, pair students with sympathetic non-EL peers.
• Provide students with illustrated bilingual dictionaries and glossaries to support understanding of tricky tier two vocabulary words, such as compare and contrast.
• Have students work in a small, teacher-led group during the last activity. Provide students with a story problem in their home language (L1) to check for understanding of mathematical concepts, such as using base-ten blocks and standard algorithm to add three-digit numbers.
• Allow students to share their remarks in their home language (L1), if possible.

• Encourage students to share their ideas without referring to the sentence stems.
• Ask students to explain the definitions of the vocabulary cards in their own words after you read them aloud.
• Have students write their answers down using short sentences during the guided practise activity.
• Encourage students to read their sentences aloud to a partner to check for accuracy and to make sure they make sense.
(5 minutes)
• Provide students with time to reflect on the two strategies (standard algorithm and base-ten blocks) as they answer the following question: "What is the most important similarity between the two strategies?"
• Have students share their responses with the class and lead a discussion/debate about which strategy makes most sense to students. Encourage students to justify their reasoning by providing students with sentence stems and frames, such as:
• The most important similarity is ____.
• I prefer using ____(insert strategy) because ____.
• It is easier for me to understand place value when I use ____Because ____.
(2 minutes)
• Wrap up the lesson up by explaining to students that we each have different ways of thinking. Say, "While I may prefer one strategy, you might prefer another. Each of our brains are unique!"
• Tell the students that mathematicians think in many different ways and by learning how to explain our thinking, we can help others solve problems that may be tricky for them!