Writing 1000

This activity will develop fluency with combinations of numbers that make 1 000. This is a useful way to help the students understand the bridge between 3-digit and 4-digit numbers.

Question 2 encourages the students to use a compensation strategy to make a series of addition equations that are equivalent to 1 000. In your discussion with them, ensure that each student can clearly see the connection between their equations.

Question 3 links addition of equal groups to an equation using multiplication to encourage more efficient ways of thinking about 1 000. This is then extended in question 4 into equations involving combinations of operations.

In question 4b, the students should discuss and share the ways they used compensation to help them derive new equations as they expanded their original equation.

Challenge the students to come up with expressions that have a pattern in them, such as:

• 40 x 20 + 20 x 10
• 8 x 50 + 4 x 100 + 1 x 200
• 60 x 30 – 40 x 20
• 50 x 25 – 20 x 10 – 10 x 5.

1.

a. Results will vary.

For example:

• 510 + 490
• 156 + 844
• and so on.

b. Results will vary.

For example:

• 100 + 300 + 600
• 236 + 552 + 212
• and so on.

2.

• 1 000 x 1 or 1 x 1 000
• 500 x 2 or 2 x 500
• 250 x 4 or 4 x 250
• 200 x 5 or 5 x 200
• 125 x 8 or 8 x 125
• 100 x 10 or 10 x 100
• 50 x 20 or 20 x 50
• 25 x 40 or 40 x 25

Discussion will vary. You will know if you have found all the possibilities when you have used all the factors of 1 000. (For example, 3, 6, 7, and 9 do not divide evenly into 1 000.

3.

a. Answers will vary.

For example:

• 700 + 500 – 200 = 1 000
• 2 100 – 1 500 + 400 = 1 000
• 1 600 ÷ 2 + 200 = 1 000
• 1 200 ÷ 2 + 400 = 1 000.

b. Answers will vary.

For example:

700 + 500 – 200 = 1 000 could be expanded to

• (70 x 10) + (50 x 10) – (20 x 10) = 1 000
• (140 x 5) + (100 x 5) – (40 x 5) = 1 000.