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Fractions Grade 7
Sharing Task - 1 • After a battle, a Jedi Knight from the Old Republic, was retuning with 3 Wookies and Two Droids (C3PO and R2D2). On the first day of their journey, the Jedi and the Wookies wanted to share 2 square waffles in a fair manner, such that each of them got the same amount. How much of a waffle should each of them get?
Fascinating Fractions • I drew this diagram by drawing a line from the top right corner of a square to the midpoint of each of the opposite sides. Then I joined these two mid points with another line. • Can you see 4 triangles in the square? • What fraction of the area of the square is each of these triangles?
Fascinating Fractions - extension • How is this made using the first square? • What shape has been created in the middle of this larger square? • What fraction of the total area of the large square does this shape take up?
Sharing Task - 2 • One of the Wookies had 4 chocolate bars, which they decided to share on the next day of their journey. However, on the following day, 2 other Jedis joined them. Can you help the Wookie divide the 4 rectangular chocolate bars among 3 Jedis and 3 Wookies?
Sharing Task-2 (continued) • How will the results change if 6 rectangular chocolate bars are shared by 1 Jedi and 3 Wookies?
Sharing Task 2 (continued) This problem has the potential to yield different sized fractional parts that need to be combined. The problem has the following possibilities when 3 Jedis and 3 Wookies share 4 bars of rectangualrcholates.
Problems – Fractions Close to 1/2 • For each situation, decide whether the best estimate is more or less than one-half. Record your conclusions with reasoning. • When pitching, Joe struck out 7 of 17 batters. • Sally made 8 baskets out of 11 free throws. • Bill made 5 field goals out of 9 attempts. • Maria couldn’t collect at 4 of the 35 homes on her paper route. • Diane made 8 hits in 15 times at bat. • Make up two similar situations and discuss with a classmate.
Problem – Fraction Riddles • A rectangle is ½ red, 1/5 green, 1/10 blue, and rest yellow. How much of the rectangle is yellow? Draw the rectangle on grid paper and record the fraction that tells which part is yellow. • A rectangle is 3/5 red. The rest is blue and yellow but not in equal amounts. What could the rectangle look like? Record the solution/solutions, the colors in terms of fractions. • A rectangle is ½ red and 1/3 blue. Also, it has one green tile and one yellow tile. What could the rectangle look like? What fractional part is green? Yellow? Record. • Make up a riddle like these for others to solve.
Problem – Cuisenaire Rods Relationships • The yellow rod is half as long as the orange rod. ( Prove this to yourself with the rods.) This relationship can be written as ½ O = Y. Find all the other pairs of hales you can with the rods and build them. Record each. • Then do the same with thirds. Eg. it takes three light green rods to make a train as long as the blue rod, so light green is one-third of blue. ( Prove it with the rods.) Record like this: 1/3B = G • Find fractional relationships for halves, thirds, fourths, and so on, up to tenths. Explain why you think you’ve found them all.
One Grain of Rice Long ago in India, there lived a raja who believed that he was wise and fair. But every year he kept nearly all of the people’s rice for himself. Then when famine came, the raja refused to share the rice, and the people went hungry. Then a village girl named Rani devises a clever plan. She does a good deed for the raja and in return the raja lets her choose her reward. Rani asks for just one grain of rice, doubled every day for 30 days. Through the surprising power of doubling, one grain of rice grows into more than one billion grains of rice – Rani teaches the raja a lesson about what it truly means to be wise and fair. Examine the different ways of expressing daily grain accumulation in terms of fractions. How will you know that your answers are correct? Hint: Create a table on the basis of facts given in the story.
