Lesson 6

Story Problems within 10

Warm-up: Notice and Wonder: Han's Cup (10 minutes)

Narrative

This warm-up prompts students to make sense of a problem before solving it by familiarizing themselves with a context and the mathematics that might be involved. Students will work with this problem in the next activity.

Launch

• Groups of 2
• Display the image.
• “What do you notice? What do you wonder?”
• 1 minute: quiet think time

Activity

• 1 minute: partner discussion
• Share and record responses.

Student Facing

What do you notice?
What do you wonder?

Han is playing Shake and Spill.
He has some counters in his cup.
Then he puts more counters in his cup.

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• If needed ask, “Will Han have more counters or fewer counters in his cup? How do you know?”

Activity 1: A Shake and Spill Story Problem (15 minutes)

Narrative

In this activity students solve a new type of story problem—Add To, Start Unknown. Students represent and solve it in any way that makes sense to them.

Monitor for students who:

• show three counters and count on to 10 or know the sum ($$3 + \boxed{7} = 10$$)
• show the total number of counters and subtract three to find the difference ($$10 - 3 = \boxed{7}$$)
• think about the story problem as $$\boxed{7} + 3 = 10$$ and use a known fact.
During the synthesis, students make sense of these different methods and relate them to the situation (MP2).
MLR7 Compare and Connect. Synthesis: After all the equations have been presented, lead a discussion comparing, contrasting, and connecting the different equations.

Required Materials

Materials to Gather

Launch

• Groups of 2
• Give students access to 10-frames and connecting cubes and two-color counters.
• Display and read the story.
• “How is the story different now than when you saw it in the warm up?” (There are numbers to show how many counters Han has in the cup and how many he puts in his cup.)
• 30 seconds: quiet think time
• Share responses.

Activity

• “Now you have time to solve the problem on your own.”
• 5 minutes: independent work time
• “Share your thinking with your partner. If you each found a different answer to the problem, work together to agree on an answer.”
• 3 minutes: partner discussion
• Monitor and select students who use the methods described in the narrative.

Student Facing

Han is playing Shake and Spill.
He has some counters in his cup.
Then he puts 3 more counters in his cup.
Now he has 10 counters in his cup.
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

Student Response

For access, consult one of our IM Certified Partners.

If students use three counters and then ten more counters and get thirteen, consider asking:

• “How did you decide how many counters to use?”
• “The story says, ‘Then he put three more counters in his cup. Now he has ten counters.’ How can you use counters to show the ten counters Han has at the end? Where are the three he added to the cup?”

Activity Synthesis

• Invite previously identified students to share in the order above.
• “How are these methods the same? How are they different?” (Two use the add in any order property. The difference is 7. I can subtract or add to find the answer.)
• If needed, “In each of these equations, it shows that the answer to the question is 7.”

Activity 2: Shake and Spill Story Problems (20 minutes)

Narrative

The purpose of this activity is for students to solve various Add To/Take From and Put Together problems with the unknown in all positions. Problems are presented through the familiar Shake and Spill context and all sums are within 10 so students can attend to making sense of each problem. Students use the commutative property, count on, take away or use known sums. When students connect the quantities in the story problem to an equation, they reason abstractly and quantitatively (MP2). During the synthesis, students focus on sharing equations and comparing the start and change unknown problems, as well as how the commutative property can help them solve story problems with an unknown start. As students discuss and justify their decisions, they share a mathematical claim and the thinking behind it (MP3).

Engagement: Develop Effort and Persistence. Chunk this task into more manageable parts. Check in with students to provide feedback and encouragement after each chunk.
Supports accessibility for: Attention, Social-Emotional Functioning

Required Materials

Materials to Gather

Launch

• Groups of 2
• Give students access to 10-frames and connecting cubes or two-color counters.

Activity

• 7 minutes: independent work time
• 3 minutes: partner discussion
• Monitor for students who write equations and can explain their thinking for Kiran’s and Clare’s problems.

Student Facing

1. Noah is playing Shake and Spill with 10 counters.
4 of the counters fall out of the cup.
How many counters are still in the cup?
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

2. Kiran has 4 counters in a cup.
He doesn’t have enough so he puts more counters in.
Now he has 7 counters in his cup.
How many more counters did Kiran put in his cup?
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

3. Clare has some counters in a cup.
She puts 3 more counters in her cup.
Now she has 9 counters in her cup.
How many counters were in her cup before she added more?
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

4. Priya has some counters in a cup.
She has 2 red counters and 8 yellow counters.
How many counters does she have?
Show your thinking using drawings, numbers, or words.

Equation: ________________________________

Student Response

For access, consult one of our IM Certified Partners.

Activity Synthesis

• Invite previously identified students to share.
• “How are the problems about Kiran and Clare the same? How are they different?” (They are the same because they both have a number of counters missing, not the total number. You can use addition or subtraction to find the answer to both. They are different because I know how many Kiran starts with and then he adds more. I don’t know how many counters are in Clare’s cup to start with, but I know that three are added to make nine.)
• If needed ask, “What equations represent these story problems?”
• “What equations represent Noah’s problem? Priya’s problem?”

Lesson Synthesis

Lesson Synthesis

“Today we solved a new type of story problem. Sometimes we do not know what number to start with. We saw equations like $$\boxed{\phantom{3}} + 3 = 9$$. How can we find the missing number in this equation?” (We can switch it to $$3 + \boxed{\phantom{3}} = 9$$ and count on from 3 until we get to 9. We can subtract $$9 - 3 = \boxed{\phantom7}$$.)

Cool-down: How Many Counters? (5 minutes)

Cool-Down

For access, consult one of our IM Certified Partners.

Student Section Summary

Student Facing

We counted on.

$$4 + 3 = \boxed{7}$$

$$4 + 3$$ is the same amount as $$3 + 4$$.

We learned that when expressions have the same value, you can show that with an equal sign.

$$4 + 3 = 3 + 4$$

We learned that we can use addition to find the difference between 2 numbers.

$$10-6= \boxed{\phantom7}$$

$$6+\boxed{\phantom7}=10$$

Since I know 6 + 4 = 10, then I know 10 - 6 = 4.