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Week 06 · Expressions

Thursday

The acorn piles
// Parentheses first, and expressions in words
⏱ about 15 min

Thursday: The acorn piles

Chris the Coyote settles by the campfire stones and adjusts the feather in his hat.

"Last autumn, Oliver counted the acorns in two great piles," he says.

"One pile had 1,894 acorns. The other had 921."

"Then Riley the Raccoon asked, what if we had three times as many acorns?"

"Riley started to add and multiply, his tail swishing busily."

"Oliver simply wrote 3 × (1,894 + 921) on a leaf."

"No need to calculate," said Oliver. "This is three times the size of both piles together."

Learn it: read an expression without working it out

1,894 + 921 is the number of acorns in both piles.

3 × (1,894 + 921) is 3 times as large as 1,894 + 921.

(1,894 + 921) ÷ 2 is half as large.

(1,894 + 921) + 10 is 10 more.

We can compare expressions like these without working them out.

Three equal groups with six dots in each group

The picture shows 3 × 6. It is 3 times as large as one group of 6.

COMPARE WITHOUT CALCULATING
  • Read the question.
  • Tap your answer.
Compare 4 × (1,250 + 36) with 1,250 + 36. Without calculating, the first is...
Compare (4,820 + 96) ÷ 2 with 4,820 + 96. Without calculating, the first is...
Compare (608 + 45) + 10 with 608 + 45. Without calculating, the first is...
Compare 7 × (305 - 18) with 305 - 18. Without calculating, the first is...
WHICH SIGN FITS?
  • Read the question.
  • Tap your answer.
6 × (25 + 48) ? (25 + 48) × 6
5 × (1,200 + 340) ? 4 × (1,200 + 340)
(980 - 75) ÷ 5 ? 980 - 75
2 × (450 + 39) ? 450 + 39 + 450 + 39
QUESTIONS ABOUT THE STORY
  • Read the question.
  • Tap your answer.
Three times as many acorns as both piles together. Which expression shows this?
Half of the acorns in both piles. Which expression shows this?
Riley fills 3 bags with 12 acorns each. He has 5 more in his paws. How many acorns?
Oliver has 25 acorns and Chris has 15. They share them equally among 8 friends. How many each?
SentenceTrue or false?
3 × (1,894 + 921) is 3 times as large as 1,894 + 921.?
(500 + 60) ÷ 2 is twice as large as 500 + 60.?
(45 + 30) + 10 is 10 more than 45 + 30.?
3 × (20 + 5) = 75?
WHY THIS EXERCISE(500 + 60) ÷ 2 is half as large as 500 + 60, not twice as large.
Try it
Count the spoons in one drawer, or the books on one shelf.
Write an expression for twice as many, like 2 × (8 + 5).
Write an expression for half as many, if the number can be split in half.
Tell a grown-up what each expression means, without working it out.
Draw the two acorn piles and write 3 × (1,894 + 921) under them.

What a story! Tomorrow Freddy has an expression game.

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