Guided Lessons

# Writing Decimal Subtraction Problems

Empower your students with the opportunity to design decimal subtraction problems with a given difference (answer). Use this lesson on its own or as support for the lesson Step By Step Decimal Subtraction.
This lesson can be used as a pre-lesson for theStep By Step Decimal SubtractionLesson plan.

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This lesson can be used as a pre-lesson for theStep By Step Decimal SubtractionLesson plan.

Students will be able to subtract decimals to the hundredths place.

##### Language

Students will be able to discuss and create decimal subtraction problems using peer interaction and sentence frames for support.

(3 minutes)
• Ask students to turn to a partner and discuss the term Decimal. Listen in on student conversations and guide them to the discovery that a decimal is one way to show fractions or parts of a whole. On a piece of chart paper, take notes on their conversations and add a few examples of decimals.
• Ask students when/where they have seen decimals in the real world and jot down students' responses on the chart paper as well. Validate students' ideas and add on any necessary points.
(12 minutes)
• Introduce the vocabulary words by showing the Vocabulary Cards one at a time on the document camera.
• Place students into partnerships. Have them read the definition to their partner, and describe the image.
• Tell students to create a sentence using each term and verbally share it with their partner. Invite a few students to share their sentences with the whole group.
• Tell them that in today's lesson, they will use these maths vocabulary terms to create situations or word problems to match a given answer. Read aloud the student-friendly content and language objective for this lesson and ask students to repeat them. Emphasize that the focus is on subtracting decimals.
• Explain to students that one common way we encounter decimals is through the use of money. Most prices in stores include a decimal to represent the cents or parts of the whole dollar involved in the price.
• Present students with a decimal subtraction word problem, such as, "Raymond is excited that he finally saved up enough money to buy rollerblades for himself. The rollerblades cost \$34.95. He has two twenty dollar bills he plans to use to pay for the rollerblades. How much money will he have left over?"
• Read the problem aloud and have students read it to themselves a second time. Rephrase the situation of the problem in a different way, for example by saying, "Raymond has two twenty dollar bills he wants to use to purchase some rollerblades and the question wants to know how much change he will get."
• Circle the keywords in the word problem that help indicate the operation needed to solve the problem such as "left over." Also, highlight or underline the numerical amounts in the problem such as "\$34.95" and "two twenty."
• Think aloud and say, "I know that two twenty dolllar bills makes 40 dollars and I need to subtract 34.95 from 40. In other words, I need to find the difference between 40 and 34.95."
• Point out to students all the steps you took to just get prepared to solve the problem. Show students how to subtract the decimal and find the answer. Emphasize the importance of changing 40 to 40.00 to have placeholders and be able to subtract the decimal. State that the answer to this subtraction problem is \$5.05: "Raymond will have \$5.05 left over after he buys the rollerblades." Direct students' attention to notice that it is helpful to answer the question in a complete sentence and provide some context to explain the number \$5.05. Tell students that by writing the answer in a complete sentence and providing some description or explanation to the answer, we are:
1. Helping to check whether our answer makes sense or not. (For example, if we were to get a number that is greater than \$34.95, we would know that it can't be the correct answer.)
2. Checking whether or not we are answering the question that was asked in the word problem.
(10 minutes)
• Tell students that in today's lesson they will have the chance to work with a partner to co-craft a situation or a word problem that matches a given answer. Remind them that all of the problems will be related to subtracting decimals and that they need to remember to line up the decimals to subtract properly and regroup when necessary.
• Model one sample for students. Display this answer on the document camera: "Lisa has \$22.55 left over after her day at the zoo."
• Show students that the answer provided is a complete sentence and it provides some context to the situation we need to create.
• Say the following:
• "I know that the answer to the subtraction problem is \$22.55. This means I need to think of a total amount to start with and then subtract a smaller amount to get \$22.55. What if I started with \$90? Then I would need to subtract \$22.55 from \$90 to get the other part of the total \$90. I line up 90.00 − 22.55And I get \$67.45. This gives me the amount I need to include in the situation I write. Here comes the fun part in which I write a story problem to match the amounts I discovered. How about, 'Lisa went to the zoo with her friend. She brought \$90 with her. She bought the tickets and some pizza to make a total of \$67.45.' Now I must ask the question. Let me check the answer again to think of how I should write the question to make sure they match. 'How much money does Lisa have left after her day at the zoo?' I reread my situation to check if it makes sense."
• Invite students to contribute their ideas and analysis of whether or not my story problem makes sense and matches the answer.
• Show students another answer statement: "Jesse has sixteen dollars and twenty five cents left after he went to the toy store."
• Lead students in a brainstorming session about possible situations that could go with this answer. Reiterate that there are many possible situations with varying numbers that would work for the answers given in today's lesson.
• Assign students an effective partner and give them a minute to think of a story problem to match this answer. Then, invite students to share their situations as you record them on a piece of chart paper. Be sure to write down the author's names next to the situation they create.
• Guide students to contribute ideas in complete sentences that provide enough context to make the situation logical and interesting.
• Affirm or correct students' maths thinking and language.
(10 minutes)
• Have students take out their maths journals or lined paper. They can either work with the same partner or you can assign them a new one.
• Assign the following four answers to a decimal word problem and have students co-create a situation for them. Clarify that both partners need to contribute ideas, but they can both write down the same situation as long as both are in agreement:
1. Henry has \$35.90 left over after he went holiday shopping.
2. Gabriela went home from the art store with \$12.75 left in her wallet.
3. Jasmin has \$58.10 left after she went to the amusement park.
4. Teo has \$21.50 left over after his outing to the movies.
• Read aloud the four problems and define any unknown words for students. Tell students to copy the answers in their maths journal or lined paper and begin co-creating a situation to go with it. Encourage students to talk about possible situations with their partner before writing anything down.
• Provide this paragraph frame to help them think of and create their story problem verbally:
• "I know that the answer to the subtraction problem is ____. This means I need to think of a total amount to start with and then subtract a smaller amount to get ____. What if I started with ____Dollars? Then I would need to subtract ____From ____To get the other part of the total ____. This gives me the amount I need to include in the situation I write."
• Remind students to show all their work. Once students have completed the four problems, combine two pairs of students to make a group of four. Have them share each other's situations and provide feedback. Model how to give feedback on the story situations and display the following sentence frames for support:
• "What if you added ____To the problem?"
• "I think you should consider changing ____To ____."
• "I like how you wrote ____In your problem."
• "Maybe you should take out the part about ____."
• After each pair in the group of four has shared their feedback, send the pairs back to make any edits or revisions to their situations until they are completely satisfied with both the maths content and the language used in the problems.

Beginning

• Display a word/phrase bank with pertinent language to be used in the lesson. Use images and examples in the bank to help solidify understanding.
• Provide bilingual resources such as online dictionaries or glossaries to help students look up unknown vocabulary words in their home language (L1) or in English (L2).
• Pair students with advanced ELs who are able to assist them in the partner activity.
• Pull aside a small group of struggling students and preteach a lesson with word problems that have a lesser linguistic load.
• Have students repeat and rephrase the directions in the lesson.

• Ask students to rephrase instructions and important learning points throughout the lesson.
• Encourage students to converse with their partners without using the sentence stems/frames for support.
• Have them be first to share their maths processes during group sharing time.
(3 minutes)
• Have a few students share their favorite situation they wrote from the independent work time.
• Ask the rest of the students to give a thumbs up if they agree that the story problem matches the answer and that the sentences make sense and flow from one to the next.
• Use this sharing session as a formative assessment to gauge students' understanding of the lesson's main points.
(2 minutes)
• Lead students in a whole class discussion with the following questions as a guide:
• What was it like to write your own maths story problems or situations? ("It was ____To write my own maths story problems because ____.")
• What did you have to do differently in creating a maths situation when compared to solving a regular maths problem? ("I had to ____When creating a maths situation which is different than solving a regular maths problem because ____.")