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measure the diameter, radius, and circumference of circles and generalize the relationships
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Gunther gathered a variety of circular objects such as container lids and wheels. For each object, he measured the diameter with calipers and the circumference with a tape measure. He started making this chart.
| Object |
Diameter (cm) |
Circumference
(cm) |
Relationship Between
Diameter and Circumfrence |
| Nut Can Lid | | | |
| Bicycle Wheel | | | |
| Oatmeal Box | | | |
He noticed a pattern in the relationship between the two measurements for each object. Estimate the relationship between diameter and circumference.
Test it by measuring the diameter of an object and predicting the circumference before measuring it. Use your calculator to find the relationship in each case. Make a rule relating the diameter and circumference
of a circle.
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solve problems involving circles (radius, diameter, and circumference)
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Elena is making a tablecloth for a round table with a diameter of 90 cm. She wants an overhang of 10 cm. How long a piece of fringe must she buy to go around the edge of the tablecloth?
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explain how time zones are determined
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Investigate how time zones are determined. Write some questions you want answered and decide where you can get the information you need. (You might use school or community libraries or computer searches, for example.) Make a report of your findings.
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determine time in various regions of the world
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If you left Vancouver at 8:25 a.m. (Pacific Standard time) and arrived in Winnipeg at 1:40 p.m. (Central Standard time), how long was your flight?
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research and report how measurement instruments are used in the community
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Make arrangements to visit businesses and services in your community. Prepare questions about how people use measurement tools. Be sure to consider all types of measure: linear, volume, capacity, area, mass, time, angles, money. Look for common and unique measures and processes of measuring. Make a report on your findings.
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design and construct rectangles, given either or both the perimeter and the area (in whole numbers)
demonstrate and generalize that many rectangles are possible for a given perimeter or given area
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Loretta wants to put 12 small square tables together to make one larger rectangular table to use for a class party. She is using square tiles to experiment before she moves the tables. Use 12 tiles to find all possible arrangements. Use grid paper to record your solutions. Make a chart to show each solution. What is the area of each large table? What is the perimeter of each large table? Which one has the least perimeter? Try the same experiment with 15 tiles, 24 tiles, 30 tiles. Compare your results. Is there a relationship between the shape of a table and its perimeter?
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Shape and Space (Measurement)
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