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How many do you see?
How do you see them?
The purpose of this activity is for students to solve a modified Compare, Difference Unknown story problem. The problem asks students to compare the quantities in the problem and then determine the size of the difference. The problem context also intentionally elicits matching strategies. Students begin the activity by looking at the problem displayed, rather than in their books. They make sense of the bigger amount and smaller amount before working on the problem, giving them an entry point for addressing both - “are there more?” and “how many more?” questions. When students open their books and work on the problem, they should have access to connecting cubes or two-color counters. In the Activity Synthesis, highlight the ways students describe how they represent each amount and how they see the difference (“how many more?”) in their representations.
This activity uses MLR6 Three Reads. Advances: reading, listening, representing.
MLR6 Three Reads
There are 9 dry erase boards.
There are 6 markers.
Are there more dry erase boards or more markers?
How many more?
Show your thinking using drawings, numbers, or words.
The purpose of this activity is for students to represent and solve Compare, Difference Unknown story problems. The problems in this activity continue to ask students to identify which quantity has more (or fewer) and how many more (or fewer) as separate questions. However, the contexts do not explicitly involve matching.
In addition to the different ways students may choose to represent the problem, listen for the ways they determine how many more or fewer. For example, students may think about determining the difference in the following ways or may come up with a different way of thinking about the difference.
Count on from the smaller quantity to the larger quantity.
()
Match the sets and then count how many don’t have a partner. ()
The equations in parenthesis illustrate a way you could annotate student thinking as they share in the Synthesis. Students are not expected to produce equations at this point in the unit.
There are 7 folders.
There are 9 pens.
Are there fewer folders or pens?
How many fewer?
Show your thinking using drawings, numbers, or words.
There are 5 pencils.
There are 8 markers.
Are there more pencils or markers?
How many more?
Show your thinking using objects, drawings, numbers, or words.
“Today we solved a new kind of story problem. How were these problems the same as the problems you solved in the past? How are they different?” (They are like “are there enough?” problems, we just have to answer “how many more?” or “how many fewer?” They were the same as problems we did before because we could think about how much more to add. It’s like an unknown addend problem. They were different because we were comparing quantities instead of putting them together or taking them apart. There are no actions.)
“Story problems that are about comparing amounts do not have actions. Nothing is added to something else or taken away in the story.”
“Today we saw that we can think about the amount that is bigger and the amount that is smaller. We saw different ways we can represent the bigger amount and the smaller amount with objects or drawings to answer ‘how many more?’ or ‘how many fewer?’”
“We call the amount that answers 'how many more?' or 'how many fewer?' the difference.”
“Compare problems have a bigger amount, a smaller amount, and a difference.”