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Week 06 · Expressions

Monday

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

Monday: Parentheses first

Oliver the Owl pushes his glasses up his beak and points to two wooden signs by Puzzle Pond.

The first sign says 2 + 3 × 4. The second sign says (2 + 3) × 4.

"These look almost the same," says Bennie the Bear. "Do they have the same value?"

"An excellent question," says Oliver. "The small curved marks are called parentheses."

"They tell us which part to work out first."

Bennie tries the first sign, and then the second.

His two answers are different! "So the marks really matter," he says.

Learn it: the order to work in

First, work out anything inside parentheses.

Next, multiply and divide, from left to right.

Last, add and subtract, from left to right.

(2 + 3) × 4: the parentheses come first. 2 + 3 = 5, and 5 × 4 = 20.

Four equal groups with five dots in each group

2 + 3 × 4: multiply first. 3 × 4 = 12, and 2 + 12 = 14.

Three equal groups with four dots in each group
INSIDE THE PARENTHESES FIRST
  • Read the question.
  • Tap your answer.
(8 + 4) × 3 = ?
(15 - 7) × 4 = ?
30 ÷ (2 + 4) = ?
(9 + 11) ÷ 5 = ?
MULTIPLY OR DIVIDE BEFORE YOU ADD OR SUBTRACT
  • Read the question.
  • Tap your answer.
8 + 4 × 3 = ?
20 - 12 ÷ 4 = ?
7 + 2 × 5 = ?
36 ÷ 6 + 3 = ?
SAME NUMBERS, DIFFERENT GROUPS
  • Read the question.
  • Tap your answer.
Which expression equals 20?
Which expression equals 14?
Which expression equals 18?
Which expression equals 4?
EVALUATE (6 + 2) × 3 - 4
  • Parentheses first, then multiply, then subtract.
  • Tap the steps in order.
1First
2Next
3Last
SentenceTrue or false?
(8 + 4) × 3 = 36?
8 + 4 × 3 = 36?
(20 - 5) ÷ 5 = 3?
20 - 5 ÷ 5 = 3?
WHY THIS EXERCISE8 + 4 × 3 is 20, and 20 - 5 ÷ 5 is 19.
Try it
Make 3 piles of spoons with 4 spoons in each pile.
Then add 2 more spoons on the side. That shows 3 × 4 + 2.
Now make 3 piles with 4 + 2 spoons in each pile. That shows 3 × (4 + 2).
Count both ways. Which way has more spoons?
Draw dots to show (2 + 3) × 4 and 2 + 3 × 4.

Well done! Tomorrow Oliver shows groups inside groups.