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Mystery Addends: Representing Word Problems
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Students will be able to use mental math to solve missing addend questions using both addition and subtraction strategies. Students will be able to represent a given missing addend word problem using a number sentence. Students will be able to identify the initial, change, and result of a word problem.
- Tell the students that today they will be reviewing fact families, or related numbers, and they will use that knowledge to help them represent missing addend word problems.
- Remind your students that an addend is a number in a problem that is being added.
- Show the example of a fact family triangle to the students, and have them explain the relationship between the 3 numbers.
- Tell the students that they will make their own fact family triangles and play a game with them.
- Pass out the triangles, and have the students each write out a fact family.
- Then, have them walk around the room to find a partner to answer the question.
- Direct each student to cover up one of the 3 numbers and show it to his partner.
- Next, have your students find new partners and do it again.
- After they have asked several peers, have them sit down.
- Instruct your students to keep the triangles in their desks to play later.
- Ask students to identify the larger number (18) and the smaller numbers (7 and 11). Model counting on from 11 to 18 as you think aloud, "11 + 7 = 18. If I know this fact, I also know that 7 + 11 = 18."
- Use manipulatives or a number line to show students that 18 - 7 = 11 and 18 - 11 = 7.
- Show students a few more examples of fact families before excusing them to make their own fact family triangles.
- Remind students that fact families include two addition and two subtraction facts. The number at the top is the sum, or total, of the two parts in the bottom corners.
- Write ____ + ____ = ____ and ____ - ____ = ____ on the board. Model solving for the third number in a fact family using both addition and subtraction.
Explicit Instruction/Teacher modeling(10 minutes)
- Write a word problem on the board similar to one on the worksheet.
- Read it aloud to the class and explain your thinking to them, reasoning how the sentences tell you the starting and ending amounts.
- Use the key terms initial, or beginning, and change, or difference, when discussing the missing addends to help the students visualize the story.
- Begin by providing a concrete model of solving for a missing addend. Use a cup and circular counters. Tell students, "I have ten circles total. I am hiding some circles under this cup. There are four circles outside the cup. How many circles am I hiding?"
- Allow students time to think about the problem and explain their thinking. Accept all answers before displaying the hidden counters. Continue with a few more examples using ten total counters.
- Define "initial" as the amount that you start with. Write __ + ? = __ on the board to guide the students in solving the problem.
- Encourage students to explain their thinking as they discuss solving the word problem. Some students may solve addend unknown problems using addition, while others may use subtraction. Accept different strategies as viable approaches for solving the problem.
Guided Practice(10 minutes)
- Write a new word problem on the board similar to the one during the explicit instruction.
- This time, have the class read out the question, and have students go through sentence by sentence to locate the addends for the initial and change.
- Ask the students to help you write down the number sentence that represents the word problem using a ∆ (triangle) to represent the mystery addend.
- Then, change the word problem a little to switch the mystery addend, and then have the students explain how they would answer that one.
- Read the problem once, and tell students to turn and talk to a partner to desribe the situation in their own words.
- If possible, provide a word problem in students' home language (L1).
- Use a question mark rather than a triangle to represent the mystery addend.
- Challenge students to explain how they might use both addition and subtraction to solve problems involving a mystery addend.
- Instruct a student write the fact family that corresponds to the word problem on board.
Independent working time(20 minutes)
- Explain to the students that they will independently do what they just practiced with you on the board.
- Handout the Missing Addend Word Problem worksheets, and have the students cut out the number sentences and match them to the word problems.
- When students finish this, instruct them to pair up and discuss why they chose the number sentence they did for each word problem.
- As the students are doing this, walk around and conference with students and document their thinking.
- When you notice that the students have done their pair-sharing, choose some students to share what they did and why.
- Read each problem aloud as a class. Sketch the scenarios presented in the word problems, and clarify unfamiliar vocabulary.
- If possible provide word problems that involve solving for a missing addend in students' L1.
- Instruct students to restate the problems using their own words to a partner.
- Invite students to write word problems that involve solving for a missing addend. Exchange problems with a partner.
- Enrichment: For advanced students, ask them to make their own missing addend word problems, and have their peers write number sentences to represent them.
- Support: Give students manipulatives, or instruct them to draw a picture of the word problem to help them visualize it.
- Make sure your students are correctly representing the missing addend word problems with number sentences.
- Walk around as your students are completing the assignment, checking their initial and change amounts.
- Ask guiding questions such as, ""How do you know that that number sentence matches the word problem?"" and ""What number should you start with?"" as students complete the matching activity.
- Encourage students to explain their thinking as they match the number sentence to the word problem. Ask them how they know that the number sentence that they chose is correct.
Review and closing(5 minutes)
- After the students share their answers as a class, write down a couple of number sentences on a piece of chart paper to show missing addends.
- Review a few examples from the worksheet. Use an illustration to show how the word problem and number sentence are connected.
- Allow students think time to solve for the missing addends in the number sentences. Model solving for the missing addend using subtraction, and then checking for accuracy using addition.