Measurement Test: Unit 5

B. What unit would you use to measure the dimensions of a skating rink? Why?

I would use metres because I know that a metre is about as big as a giant footstep. I know that if I walked across a skating rink’s length and width, the amount of footsteps would not be too big toimagine in my head. I know I wouldn’t pick centimetres because a centimetre is about as wide as my pinky finger and I know that the length and width of a skating rink are a lot bigger than the width of my pinky finger.

B.

I think I would use decametres because a skating rink would be verylong (about 30 by 100 metres). I know that a metre is one big step,so a decametre would be 10 big steps. I think it would make senseto use decametres because I know that a hockey/skating rink is morethan 10 big steps long and wide.

C. In what way is the measurement 5.60 cm like 5.6 cm? How is it different?

I know that if I put the measurement 5.6 cm in a place value chart,then it would show that there are 5 cm and 6 mm. If I put 5.60 cmin a place value chart, then it would also show that there are 5 cmand 6 mm. That is how they are the same.The difference is that 5.60 cm is being more precise and measuring tothe nearest hundredth of a metre instead of just to the nearest tenth ofa metre (5.6 cm).

D. Draw a hexagon and a rectangle that have the sameperimeter as this triangle.

The triangle has a perimeter of 12cm because each side is 4cm long.4cm + 4cm + 4 cm = 12cmI know that the hexagon and the rectangle have to have a perimeter of 12cm.

Properties of a hexagon: 6 equal sides12cm ÷ 6 = 2cm2cm + 2cm + 2cm + 2cm + 2cm + 2cm= 12cmEach side of the hexagon is 2cm long.

Properties of a rectangle: opposite sides are equal, 4 sidesGuess and check4cm + 2cm + 4cm + 2cm = 12cm SKETCH

SKETCH

E. Draw a square with a perimeter that is 4cm less than the perimeter of the triangle in Question D.

I know that all sides are equal in a square.The perimeter is 4cm less than in question D, so 12cm – 4cm = 8cm.I will divide the perimeter by 4 (four equal sides): 8cm ÷ 4 = 2cm2cm + 2cm + 2cm + 2cm = 8cm SKETCH

F. A regular hexagon and an equilateral triangle eachhave a perimeter of 60cm. What are the side lengthsof each shape?

I know that there are 3 equal sides in an equilateral triangle, so I know that I have to divide 60 by 3 to get my side lengths.60cm ÷ 3 = 20cm 20cm + 20cm + 20cm = 60cm SKETCHThe side lengths of the equilateral triangle are 20cm each.

I know that there are 6 equal sides in a regular hexagon, so I know thatI have to divide 60 by 6 to get my side lengths.60cm ÷ 6 = 10cm10cm + 10cm + 10cm + 10cm + 10cm + 10cm = 60cm SKETCHThe side lengths of the regular hexagon are 10 cm each.

G. A rectangular tablecloth is 2.5 m long. Trim is to be sewnaround the perimeter of the cloth, but there is not enough.What decrease in width will make the perimeter 0.4cm shorterif the length remains the same.

Rectangle: 4 sides, opposite sides are equalI know that the length must stay the same. The decrease in width needs to make the perimeter 0.4m shorter. Since the shorter sides are equal, the decrease must be the same.

0.4 m ÷ 2 = 0.2 m SKETCH

The shorter sides must decrease by 0.2m each, so that the perimeter decreases by 0.4m.

H. The shorter side of a rectangle is 20cm. Decreasingthe longer side by 30 cm reduces the perimeter by one half. How long are the longer sides of the original rectangle?Explain your reasoning.

Rectangle: opposite sides are equalA = C and B = DSides B and D = 20cm each Strategy: guess and check

A

B

C

D

Try Side A Side C Side B Side D Perimeter 40 cm 40cm 20 cm 20 cm 40 cm + 40 cm + 20 cm + 20 cm = 120 cm

If I decrease the longer side by 30 cm (sides A and C) 10 cm 10 cm 20 cm 20 cm 10 cm + 10 cm + 20 cm + 20 cm = 60 cm

120 cm ÷ 2 (half) = 60 cm

This guess works because the perimeter is half when the longer sides are decreased by 30 cm.

I. One side of an isosceles triangle is 15 cm shorter than the other 2 sides. The perimeter is 120 cm. How long are the sides of the triangle?

Isosceles triangle: 2 equal sidesA = BSide C is 15cm shorter than A and BPerimeter: A + B + C = 120cmGuess and checkTry Side A Side B Side C ( 15 cm shorter) Perimeter 45cm 45cm 30cm (45 – 30) 45cm + 45cm + 30 cm = 120cm

Side A = 45cm, Side B = 45cm, and Side C= 30cm

A B

C

J. Which of the two shaded polygons has a smaller perimeter? How do you know?

The shape on the left has the smaller perimeter because the shape doesnot have many horizontal and vertical “cut outs”. More “cut outs” increase theperimeter of a polygon.

Which of the two has a smaller area? How do you know?

The polygon on the right has a smaller area. It does not cover as much ofthe rectangle as the polygon on the left.

Draw a polygon with a perimeter of 92 cm inside a rectangle with a perimeter of 54 cm.