For each of the following products, without using a calculator, choose the best estimate of its value.
Multiplication of Natural Numbers using Unit Squares.
Use Diagrams to Multiply Decimals.
Before you get into this activity, I would like us understand how 2.3 x 1.5 is multiplied using diagrams. 2.3 x 1.5 = ( 2 + 0.3) x (1 + 0.5)
= (2 x 1) = 2 = (0.3 x 1) = 0.3 = (2 x 0.5) = 1.0 = (0.3 x 0.5) = 0.15
Therefore, the total area = (2 + 0.3) + (1.0 + 0.15) = 2.3 + 1.15 = 3.45
Take note of this breakdown of the numbers, their multiplication, and the addition of the separate parts to give the total.
(1.) 1.4 x 2.8
(2.) 3.2 x 1.6
(3.) 4.6 x 3.4
(4.) 5.5 x 2.9
Explore Different Ways to Multiply Decimals.
In this activity, you are going to label the area diagram below to represent (2.5) · (1.2) in other to find the product. Follow the instructions below carefully.
In this next activity, you are going to use the applet below to multiply the numbers (2.5) · (1.2).
(1.) In Calculation A, how are each of the partial products obtained? For instance, where does the 12 come from?
(2.) In Calculation B, how are the 72 and 240 obtained?
(3.) Look at the diagrams in the Challenge #1 below. Which diagram corresponds to Calculation A? Which one corresponds to Calculation B?
(4.) How are the partial products in Calculation A and the 72 and 240 in Calculation B related to the numbers in the diagrams?
(1.) In Calculation B, which two numbers are being multiplied to obtain 0.5?
(2.) Which numbers are being multiplied to obtain 2.5?
Here below are three ways of finding the area of a rectangle that is 24 units by 13 units.
(2.) How are they different?
(3.) If you were to find the area of a rectangle that is 37 units by 19 units, which of the three ways of decomposing the rectangle would you use? Why?
Complete the calculations in the applet below so that each shows the correct sum.
Here below is a rectangle that has been partitioned into four smaller rectangles. For each expression, choose the sub-rectangle whose area, in square units, matches the expression.