What's the effect?
Without calculating, is 4.5 × 2 greater than or less than 4.5?
→ Greater.
Sarah has $12.50 and earns another $4.75.
What operation?
→ Addition.
19.8 + 4.1 is approximately...
→ 24.
3.4 + 2.56 = 5.90
Correct?
→ No, it's 5.96
I am a number between 4 and 5.
When you multiply me by 0.5, you get 2.25.
What am I?
→ 4.5
Without calculating, is 4.5 × 0.2 greater than or less than 4.5?
→ Less.
A 7.5 m rope is cut into pieces that are each 0.5 m long.
What operation?
→ Division.
5.9 × 0.49 is approximately...
→ 3.
Because 6 × 0.5 ≈ 3.
7.2 − 3.85 = 4.65
Correct?
3.35
My answer is 7.2.
What could my equation be?
Possible answers:
3.6 × 2
14.4 ÷ 2
7.5 − 0.3
Which is greater?
6 ÷ 0.5
6 ÷ 2
→ 6 ÷ 0.5.
A recipe needs 0.75 kg of flour. You make 4 batches.
What operation?
→ Multiplication.
24.6 ÷ 0.51 is approximately...
→ 50.
Because 25 ÷ 0.5 = 50.
2.4 × 0.3 = 7.2
Student says: "I multiplied, so the answer should be bigger."
What's wrong with the reasoning?
→ Multiplying by a number between 0 and 1 produces a smaller quantity.
I multiplied two numbers less than 1 and got 0.72.
Give me one possible equation.
→ 0.8 × 0.9 = 0.72.
True or false:
Multiplication always makes a number larger.
→ False. Example: 8 × 0.25 = 2.
You have $20 and spend $7.85.
What operation?
→ Subtraction.
Which is more reasonable for
48.2 × 0.19?
A. 0.9
B. 9.2
C. 92
D. 920
→ B.
6 ÷ 0.5 = 3
Explain the misconception.
→ They may be treating division as automatically making the number smaller. But the question is how many 0.5s fit into 6?
Answer: 12.
I divided a number by 0.25 and got 20.
What was my original number?
→ 5
Because:
5 ÷ 0.25 = 20.
Put these in order from smallest answer to largest answer, without calculating:
8 × 0.2
8 ÷ 0.2
8 × 2
8 ÷ 2
→ 8 × 0.2, 8 ÷ 2, 8 × 2, 8 ÷ 0.2
A tank contains 18.6 L of water. Each bottle holds 0.75 L. You need to determine how many completely filled bottles you can make.
What operation? Why?
→ Division, because we're determining how many groups of 0.75 fit into 18.6.
73.8 ÷ 0.19
No calculators.
Teams get a point for an estimate and must explain it.
74 ÷ 0.2 = 370
So the actual answer should be around 390.
Actual:
388.421...
4.8 ÷ 0.12 = 0.4
Find the error without doing the division algorithm.
The quickest argument is:
0.12 × 0.4 = 0.048, not 4.8.
Therefore, the answer cannot be 0.4.
Actual answer:
40
I used exactly two of the four operations.
I started with 10.
My answer was 3.5.
What could I have done?
There are lots of possibilities.
For example:
10 × 0.5 − 1.5 = 3.5