Purpose
The purpose of this activity is to support students in counting fluently forwards and backwards in units of one or ten. They should be able to start with any two-digit number and connect counting in tens or ones with changes in the quantity.
Achievement Objectives
NA2-4: Know how many ones, tens, and hundreds are in whole numbers to at least 1000.
Required Resource Materials
- Place value materials: individual items grouped into tens, such as BeaNZ in film canisters, ice block sticks bundled with rubber bands (hundreds with hair ties), or a paper form such as Place Value People. Bundled materials are important as they allow partitioning and combining without the need for “trading” tens blocks for ones.
- Calculators
- Use a place value board to organise the materials in columns and support calculation strategies. Three-column and four-column place value boards are available here.
Activity
- Write a two-digit number on the board (or display it digitally) and tell students to make it using materials on a place value board. You might need to first explain how this is done using a smaller number (e.g. 21).
Can you make 57?
- Ask the students to enter the number on a calculator and add ten but not press = (57 + 10). Write this expression on the board.
What will the calculator show after we add ten?
If we keep pressing equals the calculator will add ten each time. What numbers will show up?
When we add ten, which digit will change, and which digit will stay the same?
Let students press equals repeatedly to see what numbers appear.
- Repeat the calculation of 57 + 10 === but with each press of = match adding ten to the material model. Write the accompanying, fully completed equations on the board (e.g. 57 + 10 = 67).
- Once you reach the 97 to 107 transition, pause and ask students what they think will happen next.
What will happen this time when you press = and add another ten?
Look for students to recognise that tens make one hundred, meaning another column needs to be added to the place value chart to record each number of hundred.
- Return to 57. Ask students to make this number again, using the place value materials, and then take ten away.
- Ask the students to enter the number on a calculator and add ten but not press = (57 - 10). Write this expression on the board.
What will the calculator show after we subtract ten?
If we keep pressing equals the calculator will add ten each time. What numbers will show up?
When we take away ten, which digit will change, and which digit will stay the same?
Let students press equals repeatedly to see what numbers appear. For example, enter 57 – 10 and press = repeatedly to create a backward counting sequence by tens, 57, 47, 37, 27, 17, 7.
- Repeat the calculation of 57 - 10 === but with each press of = match adding ten to the material model. Write the accompanying, fully completed equations on the board (e.g. 57 - 10 = 47).
- Progress to students anticipating the result of adding or subtracting ten to a two-digit number.
- Put 32 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? - Put 85 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?
- Put 32 into the calculator (Make it with materials on the Place Value Board)
- Ask students to solve problems with mixed counts of tens and ones, including additions and subtractions. Match the calculator result to the materials model. Such as:
Enter 61. Add ten. Subtract 1. Add ten, Subtract 1. What number have you got? Initially, you might provide these problems for students, before asking them to make up problems for a partner to model and solve.
Next steps
- Combine place value structure with forward and backward counting sequences by tens. Ask problems that require adding or subtracting a decade number from a two-digit number.
Examples might be:- Enter 49 into your calculator (Make with materials).
You need to add forty. How many tens make forty?
What will the number be after you add forty?
Which digit will change, and which digit will not?
Why does that happen? - Enter 62 into your calculator (Make with materials).
You need to subtract fifty. How many tens make fifty?
What will the number be after you subtract fifty?
Which digit will change, and which digit will not?
Why does that happen?
- Enter 49 into your calculator (Make with materials).
- Explore the transition over 100 and below zero using the calculator. Use both counting forwards and backwards in ten and in ones to do so. Example activities might be:
- Enter 81.
Add ten. What number do you get?
Add another ten. What number do you get?
Why do you have three digits now? (You may need to use materials to show how ten tens form 100).
Keep adding ten. What happens?
When will the hundreds digit change? Why will it change? - Enter 11.
Keep subtracting one until you reach zero.
Subtract one. What happens?
Keep subtracting one. What numbers come up?
Note: Integers are delayed until Level 4 so this is just an exploration.
- Enter 81.
Add to plan
Level Two