T4T Two-Step Story Problems
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Lesson excerpt:
NC Mathematics Standard(s):
Operations and Algebraic Thinking
Represent and solve problems.
NC.2.OA.1 Represent and solve addition and subtraction word problems, within 100, with unknowns in all positions, by using representations and equations with a symbol for the unknown number to represent the problem, when solving:
o One-Step problems:
§ Add to/Take from-Start
Unknown
§ Compare-Bigger
Unknown
§ Compare-Smaller
Unknown
o Two-Step problems involving single digits:
§ Add to/Take from- Change Unknown
§ Add to/Take From- Result Unknown
Standards for Mathematical Practice:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively
3. Construct viable arguments and critique the reasoning of others
4. Model with mathematics
5. Use appropriate tools strategically
Student Outcomes:
· I can use a number line to represent addition and subtraction word problems.
· I can solve addition and subtraction word problems using strategies related to place value.
· I can communicate how I solved problems to my teacher and classmates.
Math Language:
What words or phrases do I expect students to talk about during this lesson?
addition, count, count on, group, hundreds, ones, subtraction, tens
Materials:
· base ten blocks
Advance Preparation:
● Gather materials
Launch:
Introducing Two-Step Story Problems (13-15 minutes)
Tell this story or have it written on the board and read it.
There were 15 frogs in the pond. Some frogs jumped out. Then 8 frogs jumped in the pond. Nowthere are 20 frogs in the pond. How many frogs jumped out?
Have students come to the front of the room and act out the problem. Ask, “What do we have to find?” (how many frogs jumped out).
“How can we find the answer?”
Possible student responses:
Some students may say to put 15 and 8 in the pond and then see how many need to jump out so the total is 20.
Some may suggest trying different numbers in the blank to see what works.
After students have acted out the problem, have students write an equation to represent what happened in the problem. 15 - ? + 8 = 20.
As you do this make sure to use the action language in the problem. Possible questions:
• “When frogs jump in, what operation should we use? How do you know?
• “When frogs jump out, what operation should we use?” How do you know?
Explore
Solving Two-Step Story Problems (15-17 minutes)
The students will solve the story problems on one of the worksheets.
There are two different sheets of story problems. Each of these sheets has numbers appropriate for the 2nd nine weeks of school. The next sheet has the same problems with smaller numbers.
Give the students a copy of the story problems. Have them read problem 1 with a partner. Say, “Talk with your partner about what you know and need to know?” After 1-2 minutes ask for comments.
Students can:
• Retell the story.
• Act out the problem.
• Write an equation.
• Solve the problem with a partner.
The students can solve the rest of the problems individually or with a partner. Students need multiple experiences solving multi-step problems. The problems on the worksheets are examples. The teacher can create additional problems. As the students are working on the problems observe their strategies. Choose several students with strategies you want shared to share during the “explain” time of the lesson.
Discuss
Discussion of Strategies Used to Solve Story Problems (8-10 minutes)
After most students have solved the problems on one worksheet, bring the students together to discuss their work. Choose the problem you want to discuss. Their attention span will not allow discussion of all the problems. The teacher can record strategies on the board to save time and have the students explain their strategies.
Questions to ask:
• What do you notice about how this strategy uses place value?
• How are these two strategies alike/different?
• Why did you choose this strategy?
• Why did you start with this number?
• What’s hard about this problem?
Additional Activities (20-30 minutes)
Beat the Calculator
Introduce the game, “Beat the Calculator.” The rules and cards are attached to this game.
Students solve the problems mentally and with a calculator. Play the game with the class. One side of the class can solve the problem mentally and the other side solves the problem with a calculator. Do this several times, switching sides for using the calculator and mentally solving the problems.
After several rounds ask, “What does this game help you do?”
• Solve problems mentally.
• Practice using a calculator.
• Find easy numbers to solve first. Example in 8 + 6 + 2 the students may see that adding 8 + 2 first makes a 10 and then adding the 6 is easier.
Ask, “How do these problems relate to two-step story problems?”
After the class has worked together to solve the problems tell them that they will play the game with a partner tomorrow. This game should be played repeatedly during class time.
Evaluation of Student Understanding
Informal: Checked through questioning during the lesson. Also formative assessment is done while students are working on the worksheet. As students are working, questions to ask are;
· Where did you start? Why?
· What are the actions in the story?
· Do the actions tell you to add or subtract? How do you know?
· Does you answer make sense?
Formal: Students can be assessed formally when they are working on the Explore tasks. If you would like an extra task for an exit ticket consider posing: There are 37 girls in the gym. Then 19 girls leave. Then if 28 more girls show up. How many girls are now in the gym?
Meeting the Needs of the Range of Learners
Intervention: Students who have difficulty solving the two-step problems may need to use smaller
numbers so they can concentrate on the structure of the problem rather than the numbers. You can change the numbers to one digit numbers or numbers less than 20. Example: There were 5 students on the playground. 3 students joined them. Then 2 students went inside. How many students are now on the playground?
There are two versions of each worksheet. The second worksheet has the same word problems with smaller numbers.
Extension: Have students write two-step problems and have classmates solve the problems. An example: There were some students on the playground. 36 children joined them. In a few minutes 16 students went inside. Now there are 75 students on the playground. How many students were on the playground at the start? ( ? + 36 – 16 = 75). Start unknown problems are harder for most students to solve.
Possible Misconceptions/Suggestions:
Possible Misconceptions |
Suggestions |
Students may struggle adding or subtracting. |
Work with smaller numbers (20 or less) and provide them with base ten blocks or ten frame cards to support their work. |
Students may struggle determining whether to add or subtract. |
Students need concrete objects such as base ten blocks or ten strips. Use smaller numbers and have students discuss with classmates and you about the action of the problem to determine whether they should add or subtract. |