Teacher resources and professional development across the curriculum

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ConnectionsSession 06 Overviewtab aTab btab ctab dtab eReference
Part B

Exploring Connections
  Introduction | Try It Yourself: Area and Perimeter | The Products Game | Problem Reflection | Your Journal

 
 

Question: How does this game encourage the building of connections while solving problems?

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Our Answer:
Since the largest possible product is the goal, participants are likely to think about place value and to use rounding and estimation strategies as they think about their possible multiplication problems. This is related to checking the reasonableness of calculations.
 

Question: What connections may be made to increase students' understanding of calculation procedures?

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Our Answer:
Examining the partial products is more likely to place an emphasis on the value of the digits in a problem and may extend an understanding of place value. It may also increase students' understanding of the steps that are involved in the standard multiplication algorithm, in particular, noticing that two partial products involve a quantity of tens in two-digit problems. This leads to a better foundation for later work when multiplying algebraic expressions. For example, this can be connected to procedures for multiplying expressions, such as (x + 2)(3x - 1).
 

Question: When considering the largest product of two-digit numbers, how might you make a connection to the previous Interactive Activity involving area and perimeter?

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Our Answer:
Connecting the multiplication problem to area could facilitate students' understanding of how to maximize the product. One possibility is to use two numbers as the length and width of a rectangle. The length and width must be whole numbers between 10 and 99, and you want to make the rectangle with the largest possible area. Notice that this is the opposite of what you did in the Interactive Activity, since you're now looking to maximize the area, rather than the perimeter, in order to have the maximum product.
 

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