# Limited understanding of groupings of ten

### Diagnostic questions

Write the number 145 on a piece of paper. Ask the student to answer the following questions verbally:

- a. Tane has $145 in his savings account. His nana gives him $10 for his birthday.

b. How much money does Tane have now?

c. Which digits will change in the written number? If the student answers correctly, flip the paper and write 155. - a. If Tane has $155 and his aunty gives him another $13, how much does he have now?

b. Which digits will change in the written number? If the student answers correctly, flip the paper and write 168. - a. If Tane has $168 and he finds another $2 on the footpath, how much money does he have now?

b. Which digits will change in the written number?

### What to notice in the student’s response

Does the student solve by counting on?

Does the student identify the impact that addition has on digits within a number?

Can the student make changes within a group of ten?

Can the student answer questions that involve creating a new group of ten?

### Deliberate acts of teaching

#### Materials

- 2 dice labelled differently:

+, +, +, –, –, –

1, 10, 10, 100, 100, 1000 - Place value blocks
- Place value flip chart or place value houses

The place value system we use is based on groups of 10. In this game, students use a place value flip chart to add or subtract powers of 10 (1, 10, 100, 1000).

**Win, Lose, Draw **

This is a game that can be played several ways. If necessary, begin by using place value blocks to model each number.

Write $100 at the top of the page.

Ask the student to roll the number dice.

Ask the student to roll the operation dice to find out whether the result of the first throw will be added to or subtracted from $100.

Ask the student to change the model as required and to record the new amount. If the amount subtracted is greater than the existing total, they can record the result as 0, not as a negative number. Continue for five or ten rolls and determine whether the game was a win, lose, or draw by comparing the end result to 100.

Introduce a game element, with pairs trying to score the biggest or smallest number, or have a target number and see whether the students can reach it within a certain number of dice throws.

### What to do next if the student is stuck

Use a dice labelled with only ones and tens. Build up to a dice labelled with ones, tens, and hundreds. Omit the operation dice and add each new amount to the total.

### Initiating home-based activities

Send home a set of place value dice, along with instructions on how to play the game. Explain to the student how to record the results of the game in their homework book.

### Next teaching steps back in the classroom

Work on using place value to solve problems involving addition and subtraction. If the student reverts to counting on, ask them whether they can identify how many tens and ones a number has and discuss how these can be used to solve addition and subtraction problems.