1. From the middle of the grade 3 Math Trailblazers textbook, p. 101:

At the end of Tina's birthday party, she will give each of her guests a party bag. After she fills the bags with toys and candy, she will tie the bags with ribbon. She bought 45 inches of red ribbon and one yard of blue ribbon.

To help you answer the following questions, you should use a yardstick or rule, scissors, and ribbon or string. You may wish to use pictures, number sentences, or words. For each problem, explain how you found your answer.

1. If Tina cuts the red ribbon into pieces that are 7 inches long, how many pieces of red ribbon will she have?

2. She cut the blue ribbon into four equal pieces. How long is each piece?

3. Tina needs two more pieces of ribbon. She found one piece of green ribbon that is 7 inches long and cut it into two equal pieces. How long is each piece?

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2. From the middle of the grade 3 Singapore Math, workbook 3a, p. 138-9

A fruit seller sold 1 kg of grapes for $8. He collected $96 altogether. How many kilograms of grapes did he sell?

Tim printed 900 pamphlets. He packed them equally into 8 boxes. How many pamphlets were there in each box? How many pamphlets were left over?

8 Students sold 272 concert tickets at $3 each. Each student sold the same number of tickets. How much money did each student collect?

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Note the mandated use of concrete materials by Trailblazers, which make abstract calculations superfluous.

Note the large numbers in the Singapore problems, which make it impractical to bypass numerical calculations. Then there's the conceptual challenge of figuring out when to divide and when to multiply, and (in the third problem) of combining these into a multi-step solution.

Stone knives and bearskins vs. higher level thinking.

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