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Number Trail Grade 5 / Week 06 / Tuesday
2/6
Week 06 · Expressions

Tuesday

Groups inside groups
// Parentheses first, and expressions in words
⏱ about 15 min

Tuesday: Groups inside groups

Oliver opens a puzzle box he found under an old oak tree.

Inside is a smaller box, and inside that box is a tiny one.

"Expressions can work like these boxes," Oliver says thoughtfully.

"A group can sit inside another group."

Bennie peeks at a card in the tiny box. It says 2 × (3 + (4 × 5)).

"Where do I start?" he asks.

"Open the tiniest box first," says Oliver. "Then work your way out, one box at a time."

Learn it: work from the inside out

Find the innermost group and work it out first.

2 × (3 + (4 × 5)): first 4 × 5 = 20.

Next 3 + 20 = 23. Last 2 × 23 = 46.

Some books use other marks for the outer groups.

Brackets look like [ ] and braces look like { }.

They mean the same thing as parentheses: work inside first.

So 2 × [3 + (4 × 5)] has the same value as before.

WORK FROM THE INSIDE OUT
  • Read the question.
  • Tap your answer.
2 × (3 + (4 × 5)) = ?
((6 + 4) × 2) - 5 = ?
50 - (3 × (2 + 8)) = ?
(18 ÷ (4 + 2)) × 7 = ?
BRACKETS AND BRACES
  • Read the question.
  • Tap your answer.
3 × [10 - (2 + 4)] = ?
[(5 + 3) × 2] ÷ 4 = ?
[20 - (4 × 3)] × 5 = ?
2 × {5 + [12 ÷ (1 + 3)]} = ?
WHERE DO THE PARENTHESES GO?
  • Read the question.
  • Tap your answer.
Which expression equals 26?
Which expression equals 6?
Which expression equals 30?
Which expression equals 3?
EVALUATE 3 × (2 + (10 ÷ 5))
  • Start with the innermost group.
  • Tap the steps in order.
1First
2Next
3Last
ORDER BY VALUE
  • Work out each expression.
  • Put them from least to greatest value.
11st
22nd
33rd
44th
SentenceTrue or false?
2 × (3 + (4 × 5)) = 46?
(10 - (2 × 3)) × 2 = 16?
40 ÷ (4 × (1 + 1)) = 5?
(7 + (3 × 2)) - 1 = 19?
WHY THIS EXERCISE(10 - (2 × 3)) × 2 is 8. And (7 + (3 × 2)) - 1 is 12.
Try it
Put 2 spoons in a cup, then add 1 more spoon.
Do the same with two more cups.
Write an expression for all the spoons, like 3 × (2 + 1).
Now put all three cups in a bowl with 4 extra spoons.
Write a new expression with a group inside a group.
Draw three boxes, one inside the other, and write 2 × (3 + (4 × 5)) on them.

Great work! Tomorrow we turn words into expressions.

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