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The purpose of this Number Talk is to elicit strategies and understandings students have for subtracting within 1,000, particularly around adding up to find differences. These understandings help students develop fluency for subtracting within 1,000.
Find the value of each expression mentally.
The purpose of this activity is for students to match division expressions to division situations. Students should justify their matches by articulating how the numbers in the expression connect to what is happening in the situation (MP2).
Match each situation about spinning tops with an expression that can represent it.
1. Clare has a collection of 24 spinning tops in 4 colors. She has the same number of tops in black, white, red, and green. How many tops of each color does she have?
A.
2. Priya and her friend decorate 24 wooden tops with paint. Each person paints the same number of tops. How many tops does each person paint?
B.
3. A store has 24 tops from around the world displayed in 6 boxes. Each box contains the same number of tops. How many tops are in each box?
C.
4. Diego has 12 trompos (trohm-pohs) to give as gifts. He gives each friend 2 trompos. How many friends get trompos as gifts?
D.
5. Six friends make 12 dreidels (dray-duhls). Each friend makes the same number of dreidels. How many dreidels does each friend make?
E.
The purpose of this activity is for students to understand that the same division expression can be used to represent both types of division situations. Students are given two situations and asked to match a division expression to one of the situations, but the expression matches both situations given. It is okay if students do not recognize that the expression matches both situations in the activity, because it will be discussed in the Activity Synthesis.
Students learn that the number we are dividing by is called the divisor and understand that the divisor can represent the size of the groups or the number of groups. When students explain that a divisor can be interpreted differently based on the situation it represents, they reason abstractly and quantitatively (MP2).
Consider these 2 situations.
A. Han has 21 toy cars. He puts the same number of cars in each of 3 boxes. How many cars are in each box?
B. Han has 21 toy cars. He wants to put 3 cars in each box. How many boxes will he need?
Which situation does the expression represent? Explain your reasoning.
The purpose of this activity is for students to apply what they have learned about representations of division to match drawings and expressions to division situations (MP2). In doing so, students solidify their understanding that the same division expression can represent both types of division situations. The given drawings enable students to see the number of groups and how many objects are in each group. The work here helps students make connections across the three representations before they write their own division expressions and solve division problems in a subsequent lesson. When students describe how one equation can represent different stories, they attend to precision in the language they use and the correspondence that they establish between the equation and the stories (MP6).
Match each situation to a drawing and an expression that represent the situation. Be prepared to explain your reasoning.
Drawings
A
B
Expressions
C
D
Display some expressions from the lesson, such as and .
“Is there any way to tell the expressions that represent a ‘how many groups?’ problem from the expressions that represent a ‘how many in each group?’ problem?” (No, not by just looking at the expression. We would have to look back at the situation or the drawing.)
“Division expressions can be interpreted two ways, and we can’t really tell what type of division situation is being represented unless we have a situation or a drawing that goes with the expression.”