# Double Double Boil and Bubble

Teacher’s Notes

These exercises, activities and games are designed for students to use independently or in small groups to practise number properties. Some involve investigation and should be formally written up (LINK to investigation write-up sheet) and may become longer and more involved tasks with subsequent recording/reporting. Typically an exercise is a 10 to 15 minute activity.

### Number Framework domain and stage:

Multiplication and Division. Early additive, advanced additive, advanced multiplicative

### Curriculum reference:

Number, level 4

### Numeracy Project book reference:

These exercises and activities follow from a teaching episode based on Book 6 page 25 and Book 6 page 40. Extra teaching episodes are described with the exercise notes below.

### Materials:

- Multilink blocks
- 100s chart and flipblock 100s board
- counters
- calculator

### Prior knowledge. Students should be able to:

- explain 1x2 = 2
- double any two digit number

### During these activities students will meet:

- Place value
- multiples of 2

### Background:

Further information to back up what they will meet:

- FIO Books – Check Number Books for doubling activities.
- Digistore Activities – See http://www.nzmaths.co.nz
- National Archive of Virtual Manipulatives (via Google)

### Comments on these exercises

In exercises 1,2,3 and 6 some attempt to structure the problems to encourage use of other answers, two more and two less, close to ten strategies. Doubling is a very powerful skill, and possibly the most important following counting, that students must aquire early. The first three exercises cover all numbers from 2 to 99.

Exercise 1

Teaching lessons preceeding this exercise could include:-

- single digit doubling,
- shifting through 10, 100 and beyond,
- doubling near 10, 100, 1000
- doubling 25, 50, 75
- modelling doubling as adding same number twice and two groups the same

Exercise 2

Teaching lessons preceeding this exercise could include:-

- modelling on the 100s board that 24 for example is down 2 rows and across 4 when doubled becomes down 4 rows and across eight.
- discuss what happens at the tens change, place value.
- link halving to doubling.
- discuss and model what happens when numbers go over 100

Exercise 3

Teaching lessons preceeding this exercise could include:-

- modelling on the number line and linking length as distance from the zero to twice the length or as same length again.
- the halving could be modelled as a folded reflection

Exercise 4

Check students can use the dice to randomly generate two digit numbers.

Exercise 5

Check students can use the dice to randomly generate three digit numbers.

Exercise 6

Teaching lessons preceeding this exercise could include:-

- revision of doubling with shifts through 10 and 100 and beyond.