I left an invitation to play out for Finny. It asked him how many different ways Jack could use his magic beans in Maths. I didn’t give him any guidance, so it was up to him to figure out what he wanted to do.

## Resources

- Magic beans (we used jelly beans, blueberries and M&Ms)
- Leaves
- Alphablocks letters
- Log slices with numbers and +, x and = written on
- Rulers
- Base 10 set
- Magnatiles

## Method

Finn read the instructions and decided what area Jack could work on first. He chose area, he knew about this from measuring the area of our rainbows. Area measures the space a 2-D (flat) shape takes up.

Before I let him work out the area of his leaves, I asked him to predict which leaf he thought would have the largest area. Once he had worked out the area of the first leaf was 24 magic beans, I asked him to use that information to help him predict how many beans the other leaf would be.

Finding out the area of his second leaf.

The next thing Finny chose to line up his magic beans to see how long a line he could make.

He knew that if you were measuring how long something is, it is called **length**, but he had a go spelling the word independently.

Finny had said in the video above, that a tape measure would be the best way to measure his long line of magic beans. Unfortunately our tape measure was in Cian’s room where he was having a nap. We had to improvise and use rulers. He decided to move his ‘length’ letters to the other side of his beans, so they didn’t get in the way of measuring.

He needed three rulers to measure the line of magic beans. Finny told me each ruler was 30cm long, so he put three ten rods under each ruler.

Finn counted in tens to work out that the total length was 90. I asked him what length was measured in, he knew it was 90 cm, not 90 chimpanzees, but decided to work out how many more chimpanzees he would need to have 100 chimps.

Ioan joined us and offered his suggestion for how Jack could use the magic beans. He suggested splitting the beans in to equal groups. Finny made 4 equal groups of 5 and Yoshi made 5 equal groups of 4. Even though the numbers were being multiplied in a different order, the answers were the same.

I challenged them to each find a different way of making equal groups that equalled 20. Ioan made 10 equal groups of 2 (he accidentally calls is 5 equal groups of 2 in the next video and I didn’t notice the mistake) and Finn made 2 equal groups of 10. I asked them if they knew a symbol that represented ‘lots of’ or ‘groups of’. They knew it was a times sign, or x.

Amid lots of giggles, they each wrote the number sentence that represented their magic beans. Finny wrote 2 x 10 and Ioan wrote 10 x 2. I asked them what you could call the 2 x 10 and 10 x 2 and Ioan said, “Inversible”. He mixed up the terms “*reversible*” and “*inverse*“. I was looking for the fact that the numbers being multiplied can be swapped around, or reversed, because they are in the same fact family.

A **fact family** is a set of four related multiplication and division facts that use the same three numbers. In this case, the fact family for 2, 10 and 20 is a set of four multiplication and division facts. Two are multiplication facts, whereas the other two are division facts:

- 2 x 10 = 20
- 10 x 2 = 20
- 20 divided by 2 = 10
- 20 divided by 10 = 2

Multiplication and division are **inverse operations**. Start with 2, then multiply it by 10 and we get 20. Now divide 20 by 10 and we get back to 2.

Finny decided to make another set of equal groups with his magic beans. This time he made 5 groups of 3. He knew that the total for 5 times 3 was 15. I asked him if he could make 15 with another type of sum, like an addition. He suggested 1+2+3+4+5.

He set out his magnatiles to show me that 1+2+3+4+5 equalled 15.

Then he showed me that he could rearrange the magnatiles by swivelling three around, making a rectangle. He then turned them in to arrays. At the end of the video he was in his own little world (the bum expert waggling of a golden goose gave it away!) but eventually heard the question.

Finny then decided to make a really big rectangle.

I asked him to work out how big the rectangle was and he counted all the individual magnatiles. I demonstrated how he could count in fives to get the answer more quickly.

His finished tray:

## DfES Outcomes for EYFS and National Curriculum (2013)

### Numeracy Year 1 programme of study

#### Number – addition and subtraction

- read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
- add and subtract one-digit and two-digit numbers to 20, including zero

#### Number – multiplication and division

- solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

#### Number – measurements

- measure and begin to record lengths and heights

### Numeracy Year 4 programme of study

#### Number – measurements

- find the area of rectilinear shapes by counting squares