Guided Lessons

# Discussing Subtraction Strategies

Get your students comfortable with discussing multiple strategies to solve subtraction problems with this lesson on two- and three-digit subtraction. It may be taught independently or as support for the lesson Subtraction with Regrouping.
This lesson can be used as a pre-lesson for theSubtraction with RegroupingLesson plan.

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This lesson can be used as a pre-lesson for theSubtraction with RegroupingLesson plan.

Students will be able to use two different strategies to subtract two- and three-digit numbers.

##### Language

Students will be able to discuss and compare subtraction strategies using peer support and sentence starters.

(3 minutes)
• Read aloud a subtraction word problem such as the following: "Mabel and her friends made 127 bracelets. They sold 98 of them. How many bracelets do they have left?"
• Lead students in a think-pair-share and have them talk about the information presented in the problem and strategies they might use to solve it. Give students time to reflect independently on the problem before assigning them a partner and having them talk to their partner about the problem.
• Invite students to share what they said or what their partner commented on in the lesson. Record their ideas on a piece of chart paper and leave it up for the remainder of the lesson. Validate their responses to the problem as they arise.
• Tell students that today they will learn two strategies to solve two- or three-digit subtraction problems and compare their strategies with their partners work.
(10 minutes)
• Explain to students that they will learn or improve their understanding of some vocabulary words related to the lesson. Tell them that they may already know the meaning of some of the terms but by spending time making meaning of them, their understanding will deepen and will help them to become stronger mathematicians.
• Introduce each vocabulary word by displaying the Vocabulary Cards. Leave the cards displayed for the rest of the lesson. Read each word and its definition. On the document camera, show students how to complete a Frayer Model using the word Solution. Read aloud the definition, draw a picture or model to further make meaning of the word, and provide examples/non-examples to students.
• Place students into partnerships. Give each pair a blank Frayer Model. Assign one of the remaining vocabulary words to each pair of students. Note: you may have to repeat words. Instruct them to fill out each section of the model collaboratively, meaning they should discuss the image, example, and non-example they add to the model. Tell students that they should copy the definition from the Vocabulary Cards onto their Frayer Model. Make sure that each student participates in the work equally.
• Have each pair of students present their completed model briefly to the whole group. After the presentations are complete, read aloud each vocabulary term and have students show you a thumbs-up if they feel that they have a strong understanding of the word, a thumb to the side if they feel they somewhat understand it, and a thumbs-down if they do not understand the term. Encourage students to be honest in their self-assessment of the vocabulary terms. Note which students may need vocabulary support throughout the lesson.
(10 minutes)
• Tell students that today there are two subtraction strategies that they will learn. One is called Expanded Notation and the other is called the Standard Algorithm. Note: students should have some familiarity with these terms after the Frayer Model activity.
• Show students on a piece of chart paper an example of how to solve a three-digit subtraction problem using both strategies (e.g., "There are 382 students in our school. 137 take the bus to school. How many students do not take the bus?"). Read aloud the problem and demonstrate how to solve it.
• Expanded Notation Subtraction (breaking apart numbers based on their place value and subtracting each part of the number). First, 382 becomes 300 + 80 + 2And 137 becomes 100 + 30 + 7. Then, we subtract the ones, the tens, followed by the hundreds. Emphasize the regrouping required in the ones section. Finally, we add the three differences we found in each place value to find the total difference.
• Standard Algorithm Subtraction (lining up the two numbers on top of each other and then subtracting from right to left, with regrouping as necessary): 382 - 137 = 245. First, I subtract the ones, the tens, and then the hundreds.
• Have students turn to their partner and compare the two strategies used to subtract. Ask the following questions and provide the sentence starters as an aid to help them compare.
• How are the two strategies similar? ("The strategies are similar in that they both...")
• How are the two strategies different? ("The expanded notation strategy is... while the standard algorithm strategy is...")
• Invite students to share their discussion with the whole class and document their observations on another piece of chart paper.
• Distribute a piece of blank copy paper to each student and have them fold it in half (hamburger style). Inform them that they will solve a subtraction problem using both strategies, one on each side of the paper. Tell students to make sure they label both types of methods on their paper.
• Show students the following problem and read it aloud (define any unfamiliar term as needed): "Samir has been saving all year to buy a new bicycle. He was able to save \$447. He decided to buy a bicycle that cost \$339. How much money does he still have left after he bought the bicycle?"
• Circulate to make sure students are using both strategies and working together with their partner.
• Ask one pair of students to come up to the document camera to share their two strategies for solving the problem. Provide them with transition words to help them share out ("First, we... Then, we... After that, we... Finally, we...").
• Ask students if anyone has AnotherStrategy they think would work well for this problem. Invite students to share any additional subtraction strategies and document their responses (ideas include drawing a base-ten model, breaking the number into friendlier numbers, etc.). Acknowledge other strategies and point out the value of having a tool box with ample methods of solving the same problem so that we become confident and flexible maths thinkers.
(10 minutes)
• Facilitate a Number Talk activity for students. Place students into A–B partnerships. Tell students that Partner A will solve the problem using the Expanded Notation strategy while Partner B will solve the same problem using the Standard Algorithm. Read aloud and display this problem: "Michelle collects stamps. She has 563 stamps from around the world. She decides to donate 269 of them to a museum. How many stamps does Michelle have left?"
• Hand out whiteboards and markers to each student. Have them solve the problem using their assigned strategy on the whiteboards.
• Have the pairs share their strategies and answers with each other, and discuss any challenges they encountered. Provide the transition words mentioned earlier. Ask students to share their processes with the whole group and jot down their observations on a piece of chart paper.
• Give students another problem and have them switch strategies (i.e., Partner A now uses the Standard Algorithm and Partner B will use the Expanded Notation strategy): "The orchard has 786 trees. 339 of them are apple trees and the rest are peach trees. How many peach trees are there in the orchard?"
• Allow time for students to complete the subtraction problem on their whiteboards. Repeat the process of sharing and comparing their strategies and answers. Give students access to the questions and sentence starters used in the Guided practise. Circulate and correct any mistakes. Continue to record students' observations.
• Hold a class discussion about their preferences for the various strategies. Give sentence frames as support:
• "I prefer the ____Strategy because..."
• "I dislike the ____Strategy because..."
• "I find the ____Strategy easiest because..."

Beginning

• Let students restate key learning points throughout the lesson.
• Allow students to use the Vocabulary Cards and/or Glossary as a reference at their desk.
• Place beginning students with a supportive partner, preferably one who speaks the same home language (L1).
• Simplify the linguistic load of the word problems.
• Ask students to state the step-by-step method of each strategy using their L1 or L2.
• Allow students to do the assessment with a supportive partner.

• Let students discuss the subtraction strategies without the support of the sentence stems/frames.
• Tell students to repeat or rephrase the directions of each section of the lesson.
• Encourage students to be the first ones in the group to explain other subtraction strategies they use.
(4 minutes)
• Pass out a sticky note to each student. Give students the problem 566 - 289 = ? And have them solve it using the strategy of their choice on the sticky note.
• Invite some students to share the strategy they chose for the assessment problem and then demonstrate how they solved it.
• Have them place their sticky note on a piece of chart paper as they exit the classroom. You can use the sticky notes to compare students' preferences for each strategy.
(3 minutes)
• Ask students to think of other operations for which they know multiple methods or strategies to solve. Have them name a few strategies that they know (e.g., arrays and repeated addition for multiplication, number lines for addition, etc.).
• Remind students about the importance of knowing multiple strategies to solve the same problem. Knowing different ways to get to the same answer helps students check their work to make sure it is correct. Being confident in multiple maths strategies makes them strong mathematicians too.