Counting sequences with three-digit numbers

1.

Write a three-digit number (e.g., 357) on the board and show students how to make it with blocks or other place value materials on a place value board. Provide time for them to make the number using materials.

2.

Ask the students to enter the number on a calculator and ask them to add one hundred, but not press = (357 + 100).

• What will the calculator show after we add 100?
• If we keep pressing equals, the calculator will add 100 each time. What numbers will show up?

Let students press equals repeatedly to see what numbers appear.

Repeat the calculation of 357 + 100 === but with each press of =, add 100 to the material model. Record accompanying equations as students tell you the answer (e.g., 357 + 100 = 400).

3.

Ask the students to enter the same number on a calculator and ask them to subtract one hundred, but not press = (357 − 100).

• What will the calculator show after we subtract 100?
• If we keep pressing equals, the calculator will take away 100 each time. What numbers will show up?

Let students press equals repeatedly to see what numbers appear.

Repeat the calculation of 357 − 100 === but with each press of =, take away 100 from the material model. Record accompanying equations as students tell you the answer (e.g., 357 − 100 = 357).

4.

Repeat these steps with adding and subtracting ten. Look for students to anticipate what happens next.

• When we add/take away ten, which digit will change, and which digits will stay the same?
• Is it always true that the hundreds digit stays the same?
• When does it change?
• Why does it change?

When you get to a through-hundreds transition in addition (e.g., 397 + 10 = 407), ask students to pause and consider what will happen when another ten is added.

Look for students to recognise that ten tens make one hundred, meaning a group of ten added to 9 groups of ten will make ten tens. On a place value board, this means one more ten will be added to the middle column of your three-column place value board. Demonstrate this and emphasise that the tens column now contains ten tens, which can be renamed as one hundred, and replaced with one hundreds block in the hundreds column. This means that zero acts as a placeholder in a number like 407.

When you get to a through-hundreds transition in subtraction (e.g., 307 − 10 = 297), ask students to pause and consider what will happen when another ten is taken away. Use the materials to demonstrate decomposing a unit of 100 into ten tens, removing one ten from the hundreds column, and then moving the remaining nine tens to the tens column.

5.

Progress to students anticipating the result of adding or subtracting units of one hundred, ten, or one to a three-digit number.

Put 769 into the calculator. (Make it with materials on the place value board.)

• Add ten. What number will you get?
• Add another ten. What number will you get? etc. (Pay particular attention to the 799 to 809 transition.)

Put 325 into the calculator. (Make it with materials on the place value board.)

• Subtract ten. What number will you get?
• Subtract another ten. What number will you get? etc. (Pay particular attention to the 305 to 295 transition.)

6.

Ask students to work in groups to pose and solve problems with mixed counts of hundreds, tens and ones, including additions and subtractions, and match the calculator result to the materials model. Such as:

Enter 458.

• Add ten. Subtract 100. Add ten. Add 10. Subtract 1.
• What number have you got?

1.

Combine place value structure with forward and backwards counting sequences by hundreds and tens. Ask problems that require adding or subtracting a century or decade number from a three-digit number.

Examples might be:

Enter 235 into your calculator. (Make with materials.)

• You need to add sixty. How many tens make sixty?
• What will the number be after you add sixty?
• Which digit will change, and which digits will not?
• Why does that happen?

Enter 496 into your calculator. (Make with materials.)

• You need to subtract seventy. How many tens make seventy?
• What will the number be after you subtract seventy?
• Which digit will change, and which digits will not?
• Why does that happen?

2.

Explore the transition over 1000 using the calculator. Use both counting forwards and backwards in one hundreds, in tens, and in ones to do so. Example activities might be:

Enter 734.

• Add one hundred. What number do you get?
• Add another one hundred. What number do you get?
• Add another one hundred. What number do you get?
• Why do you have four digits now? (You may need to use materials to show how ten hundreds form 1000.)
• Keep adding one hundred. What happens?
• When will the thousands digit change next? Why will it change?

Enter 804.

• Keep subtracting one until you reach 800.
• Subtract one. What happens?
• Keep subtracting one. What numbers come up?