Sugar, Sugar!

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Objective

SWBAT show strategies to solve problems with numbers on the decade.

Big Idea

Students explore how they could arrange their cubes to solve story problems with numbers on the decade. This exploration pushes them to understand how arranging into tens helps them solve story problems with big numbers!

Setting Up the Learning

5 minutes

This lesson is aligned to 1.NBT.C4, which asks students to add numbers within 100 using either models/drawings based on place value, properties of operations and/or the relationship between addition and subtraction. This lesson really sets kids up to be able to solve based on place value. The opening warm up and the problems all ask kids to think about how they can represent a number so that they can use it to efficiently solve story problems!

Review:

We have been working on addition and subtraction all year. They are so important because they help us figure out tricky problems in our lives. But today we are going to look at number sentences with really big numbers in them!

Connect:

Great mathematicians have to be able to solve problems with big numbers! In second grade, you will solve story problems with numbers in the hundreds! The work we do today will help prepare you for that.

Objective:

Today we are going to solve a problem together. Your thinking job is: How can I arrange my cubes to help me solve story problems with big numbers? 

Opening Discussion

10 minutes
To help students think about how we structure number, I'll have them do a quick warm-up, number sense activity. Flexible problem solvers can think of one number in a variety of ways. What I want students to see in this activity is that using base 10 helps them structure a number more quickly than any other way of representing it.
Directions:
Give students a paper, have them fold it into fourths. Tell students you want them to show 4 ways they could show the number 24 without numbers. They can only use pictures.

Student Work Time: Students show 4 ways of representing this number. While students work, I'll record 4 ways on my own chart paper.

  • In one of the chart’s squares, show 24 random dots.
  • In another, show how a student drew 24 dots in one big line.
  • In another, show how a student drew dots in some organized fashion (preferably tens). 
  • In the last square, show how a student made 10s. (as in they just drew two tens and 4 ones)

Student Debrief

10 minutes

I'll have students debrief each of the 4 ways I represented 24. As we go through the chart, we are focusing on how efficient it is to represent the number that way. This will help them as they think about solving problems with numbers that are bigger. If they use random cubes, it will get confusing and "clunky". This activity helps them see that!

Thinking job: I want us to figure out which representation helps us easily count the 24.  

 See attached image for our class chart!

Random Dots: Push students to see that you get mixed up when you count these.

  • If someone walked in here, would he know there are 24 here without having to count? Why not?  

 

24 dots in a line: 

  • If the principal walked in here, would he just know there are 24? Why not?
  • Which one would be easier to count? The first one, or the second one? 

 

Arranged in groups of 10 dots: Push students to see that you can group count, but you have to verify that each group has 10 first.

  • How about the third square-How is this one different from the other two?
  • How many dots are in each group? How could you count these groups of 10?
  • Which one is the easiest so far to figure out that there are 24?

 

Tens and Ones: This person drew bars of 10 cubes each. They wrote a 10 on it to show me that it has 10 inside it.  

  • Which one is easiest now? Which one was the hardest one to count quickly? 

Connect to problem solving: Which one was the hardest ones to count quickly? Since that one was the most difficult, I am not going to use that strategy as I solve my problems today.

Problem Solving

15 minutes

Every student may not be ready for base ten in problem solving yet. I attached a Strategy Level Guide.docx. It shows the different levels of understanding that you might see with students. It also lists some ideas for "push" questions and how you can encourage students to try more efficient strategies. 

Each group will get 3 problems to solve. The last one is subtraction to make sure students are paying attention to the action of the problem. I differentiated the work based on number.

Group A: Intervention

Students get low numbers on the decade only. For example, students try 10 and 10, 20 and 10. 

Group B: Right on Track

Students get numbers on the decade under 50.

  • A push for this group is for them to use counting on by tens to help them solve. Watch the attached Group B Student Counting video to see how I worked with one student to push him to use counting on by 10s instead of counting on by 1s!

Group C: Extension

Push students to use numbers that have a number in the ones place. For example, 45 and 30. 

  • Students in this group may start using known facts to help them solve. See attached video for how I made sure a student count explain why 4+4 = 8 so 40+40=80. This is aligned to CCSS MP3, "Construct viable arguments..."; students should always be able to back up their own thinking! This discussion is also aligned to MP7, students are using the structure of the base 10 system to help them solve the problem!

See attached story problems! I left blanks for the numbers so you can decide what numbers are best for your students!

 

Closing

10 minutes

Students come back together and do a strategy share. I will have 2 students share their work with a class and we will make a strategy anchor chart. We will post this anchor chart so students can revisit it throughout the unit. First graders need these visuals to help them revisit the strategies later-it provides a mental picture of what their peers were thinking. 

 

See the Student Strategy Chart for the strategies we shared!