Question

1. mika drew this shape. what is the name of the shape mika drew? mika then drew a shape that has 2 fewer sides. what is the name of that shape? image of green octagon 23. higher order thinking how can adding doubles help you multiply by 2? give an example. 24. write the expressions in the correct column. chart with columns product is 10, product is 12, product is 35; and expressions 2×5, 7×5, 6×2, 2×6, 5×2, 5×7

Explanation:

Question 22

Step1: Identify first shape's sides

The green shape has 8 sides. A polygon with 8 sides is an octagon.

Step2: Calculate sides of second shape

8 - 2 = 6 sides. A polygon with 6 sides is a hexagon.

Step1: Define adding doubles and multiplying by 2

Adding doubles means adding a number to itself (e.g., \(a + a\)). Multiplying by 2 is \(2\times a\), which is equivalent to \(a + a\).

Step2: Give an example

Take \(3\times2\). Adding doubles: \(3 + 3 = 6\). Multiplying: \(3\times2 = 6\). So \(3\times2\) is the same as \(3 + 3\), showing adding doubles (3 + 3) helps find \(3\times2\) (result 6).

Step1: Calculate each product

• \(2\times5 = 10\), \(5\times2 = 10\) (commutative property)
• \(6\times2 = 12\), \(2\times6 = 12\) (commutative property)
• \(7\times5 = 35\), \(5\times7 = 35\) (commutative property)

Step2: Categorize into columns

• Product is 10: \(2\times5\), \(5\times2\)
• Product is 12: \(6\times2\), \(2\times6\)
• Product is 35: \(7\times5\), \(5\times7\)

Answer:

First shape: Octagon; Second shape: Hexagon

Question 23