# A jar of teddies

How many teddies are in the jar? How many teddies could you fit in your classroom?

In the image below, there are several different views of a jar that has been filled with teddies.

Can you estimate how many teddies there are in the jar?

Click below to see some different methods you might use to estimate it.

Once you have made your estimate, click to reveal the exact number of teddies in the jar!

The bottom of the jar is 10cm square, and the jar is filled to a height of 16cm.

If we wanted to design a jar that would hold 100 teddies, what dimensions could it have?

Here is another teddy:

The larger teddy is 16cm tall, 19cm wide, and 12cm from front to back.

How many teddies like this do you think you could fit inside your classroom?

What other mathematical questions could you explore?

Can you estimate how many teddies there are in the jar?

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Click below to see some different methods you might use to estimate it.

There are six different colours of teddy. I think there are around 8 to 10 of each colour. So there's between 48 and 60 teddies altogether.

There are about seven teddies visible on the top layer, and in the side view I counted around seven layers, so there must be about 50 teddies altogether.

I can see about fourteen teddies in the side view. There are about four layers of teddies going back, so there must be around $14 \times 4 = 56$ teddies altogether.

A teddy would fit in a 4cm by 4cm by 2cm space, which has a volume of 32 cubic centimetres. The jar is around 10 by 10 by 16 cm, which is 1600 cubic centimetres. 1600 divided by 32 is 50, so there are around 50 teddies.

There are about seven teddies visible on the top layer, and in the side view I counted around seven layers, so there must be about 50 teddies altogether.

I can see about fourteen teddies in the side view. There are about four layers of teddies going back, so there must be around $14 \times 4 = 56$ teddies altogether.

A teddy would fit in a 4cm by 4cm by 2cm space, which has a volume of 32 cubic centimetres. The jar is around 10 by 10 by 16 cm, which is 1600 cubic centimetres. 1600 divided by 32 is 50, so there are around 50 teddies.

Once you have made your estimate, click to reveal the exact number of teddies in the jar!

There are 55 teddies in the jar.

The bottom of the jar is 10cm square, and the jar is filled to a height of 16cm.

If we wanted to design a jar that would hold 100 teddies, what dimensions could it have?

Here is another teddy:

Image

The larger teddy is 16cm tall, 19cm wide, and 12cm from front to back.

How many teddies like this do you think you could fit inside your classroom?

What other mathematical questions could you explore?

One way to improve your estimation is to start with a number that you know is too small, and one you know is too big, and then see if you can narrow it down from there.

Can you use the ruler in the picture to work out any useful measurements?

Does it help to work out the approximate volumes?

Can you use the ruler in the picture to work out any useful measurements?

Does it help to work out the approximate volumes?

Thank you for all of the solutions we received to this problem.

Click to see solutions which estimate the number of teddies in the jar

We had these solutions come in from the International School of Brussels:

Jonathan:

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Jonathan:

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Click to see solutions for finding the size of the jar which would hold 100 teddies, using the volume of one teddy

Elmhurst School for Boys UK

The boys calculated a volume of 100 bears which was 3200cm cubed.

Then, they found the dimensions of different jars: 32 x 10 x 10 or 16 x 20 x 10 or 8 x 20 x 20 which would have sufficient capacity to hold all of the bears.

St. George's

The jar needs to have a volume of approximately 3,200cm cubed. Height 32cm width 10cm length 10cm.

Click to see solutions for finding the size of the jar which would hold 100 teddies, using the the first jar and proportional reasoning

Miss Barlow's Class, Queen Anne's School, UK (error highlighted, but good method)

Theo from Gospel Oak (UK) (error highlighted, but good method)

160 cm$^3$ is actually only the space for 55$\div$10 = 5.5 teddies

Elmhurst School for Boys UK

The boys found the volume for 55 teddies which was 1600. They divided by 55 and multiplied by 100. This gave them 2900cm cubed approximately. Then they found jars which would create this capacity.

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Theo from Gospel Oak (UK) (error highlighted, but good method)

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160 cm$^3$ is actually only the space for 55$\div$10 = 5.5 teddies

Elmhurst School for Boys UK

The boys found the volume for 55 teddies which was 1600. They divided by 55 and multiplied by 100. This gave them 2900cm cubed approximately. Then they found jars which would create this capacity.

Click to see solutions for finding the number of teddies which would fit into a classroom, using the volume of one teddy

Churchfields Junior School (London)

Big Teddy = 16 x 19 x 12 = 3648cm$^3$.

Classroom = 280 x 710 x 840 = 166,992,000$^3$.

Using rounding we know the Teddy is approximately 3600cm$^3$ and the classroom is 166,000,000$^3$.

Therefore the volume of the classroom divided by the volume of bears gives us an answer of approximately 46,111 bears would fit in.

However, pupils did say this is assuming the classroom is completely empty. Moreover, we have cupboard space, which is not included in the volume and window sills that would affect the total amount.

Elmhurst School for Boys UK

First we found the volume of a teddy bear which is 3648cm cubed. The length of our room was 7m, the width was 3m and the height was 2.8m. We calculated the volume for this which was 58.8 cubic metres. We divided 58.8 million cubic centimetres by 3648 and we got 16118 with a remainder which we rounded to 16119.

Lady Boswell's Primary

How many teddies can fit in our classroom?

First we found the volume of the classroom. Volume of Classroom: 2.3 x 8.5 .8 = 1564 m$^3$.

Then we realised we had to convert this into cm because the measurements of the teddy were in cm. Volume of classroom = 156, 400,000 cm$^3$.

Then we calculated the volume of the teddy. Volume of teddy: 19 x 12 x 16 = 3648 cm$^3$ .

Then we calculated the number of teddies by: Volume of classroom divided by Volume of teddy.

156,400,000/3648 = 42,873 teddy bears to the nearest whole. We rounded our answer.

We decided not to include the sloped part of the roof and the cupboards. It was a lot of teddy bears. We could have fitted more in if we had squashed them together so it would have been more accurate if we had been using a cube.

St. George's

We roughly measured our class and estimated the volume, Class is 800cm by 650cm by 300cm.

We worked out the volume of the teddy. Then, we rounded to help us divide. We think we can fit 39,000 teddies in.

We estimate it would take 41,000 teddies to fill our classroom which has a volume of 150m cubed. So we rounded the measurements of teddy to calculate the volume of teddy.

We then calculated volume of classroom and then converted in cm. Then divided volume of class by volume of teddy.

Some people raised concerns about using the volume of one teddy:

Haze, Iromic Schule, Germany:

But then you have to account for the teddie-air ratio

Sophie, Woodland School Basildon, UK:

The bears will compress so the volume will be variable

What about using the first jar of teddies and proportional reasoning to estimate the number of teddies that would fit in your classroom?

Click to see questions which could be investigated

St George's

How many Bears would fit in the classrooms in KS2? We could share the answers from today and add them together!

How long would it take to physically fill the rooms with teddies?

If a square classroom had a width of 17m and 3m tall how many bears would fit?

Meg, Gosel Oak

How many small teddy bears can fit in a big teddy bear?

Newbottle and Charlton Primary School

How many of the small bears could fit in the classroom?

How many big bears could in a mini bear?

How many dice could you fit in the classroom?

Claire, Meadowdale Academy:

How many chocolate bars fill your office?

How many pencils can you fit in your bin?

How many pigs can fit in your school?

How many gluesticks can you fit in an average pencil case?

Class 6B, Scotby, England

How many 5ft tall children can you fit in a double decker bus?

How many standard size hb pencils can you fit in 1 single layer class tray?

How many Bears would fit in the classrooms in KS2? We could share the answers from today and add them together!

How long would it take to physically fill the rooms with teddies?

If a square classroom had a width of 17m and 3m tall how many bears would fit?

Meg, Gosel Oak

How many small teddy bears can fit in a big teddy bear?

Newbottle and Charlton Primary School

How many of the small bears could fit in the classroom?

How many big bears could in a mini bear?

How many dice could you fit in the classroom?

Claire, Meadowdale Academy:

How many chocolate bars fill your office?

How many pencils can you fit in your bin?

How many pigs can fit in your school?

How many gluesticks can you fit in an average pencil case?

Class 6B, Scotby, England

How many 5ft tall children can you fit in a double decker bus?

How many standard size hb pencils can you fit in 1 single layer class tray?

Click to see solutions which investigate their own creative questions

Annabelle and Darcie and Lauren, Isabelle and Chloe, Jersey College for Girls

The question we wanted to answer was how many large teddies could we fit around the equator of the earth. To do this we used our knowledge that the width of the teddy is 19cm and we googled the circumference of the earth

which is 40,075km. We noticed to divide these two numbers we would have to convert 40,075km to cm so they have the same units. So we multiplied it by 100,000 and we got the answer 4,007,500,000cm. Then we divided that answer

by 19cm and got 210921052.6 teddies. As you can't have part of a teddy bear and we couldn't fit another teddy bear in we rounded down so we can fit 210,921,052 teddy bears around the equator.

Click here to see Lauren, Isabelle and Chloe's diagrams

Scarlett and Mae, Jersey College for Girls

Click here to see poster

Tino and Camilla, Jersey College for Girls

Click here to see poster

The question we wanted to answer was how many large teddies could we fit around the equator of the earth. To do this we used our knowledge that the width of the teddy is 19cm and we googled the circumference of the earth

which is 40,075km. We noticed to divide these two numbers we would have to convert 40,075km to cm so they have the same units. So we multiplied it by 100,000 and we got the answer 4,007,500,000cm. Then we divided that answer

by 19cm and got 210921052.6 teddies. As you can't have part of a teddy bear and we couldn't fit another teddy bear in we rounded down so we can fit 210,921,052 teddy bears around the equator.

Click here to see Lauren, Isabelle and Chloe's diagrams

Scarlett and Mae, Jersey College for Girls

Click here to see poster

Tino and Camilla, Jersey College for Girls

Click here to see poster

### Why do this problem?

This low threshold high ceiling task is designed to help students develop their estimation skills. Estimation is a hugely useful and important skill in all walks of life. This playful context provides an engaging hook in which to explore the big ideas of approximation and large numbers.### Possible approach

Show the images of the jar of teddies and the single purple teddy. (Before inviting students to estimate the number of teddies, you might simply ask "What do you see?" and allow some time to share thoughts.)"Estimate how many teddies there are in the jar."

Give a few minutes of individual thinking time before encouraging students to share their thoughts with a partner, then with the wider group. Here are some examples of the sorts of methods that might emerge:

"There are six different colours of teddy. I think there are around 8 to 10 of each colour. So there's between 48 and 60 teddies altogether."

"There are about seven teddies visible on the top layer, and in the side view I counted around seven layers, so there must be about 50 teddies altogether."

"I can see about fourteen teddies in the side view. There are about four layers of teddies going back, so there must be around $14 \times 4 = 56$ teddies altogether."

"A teddy would fit in a 4cm by 4cm by 2cm space, which has a volume of 32 cubic centimetres. The jar is around 10 by 10 by 16 cm, which is 1600 cubic centimetres. 1600 divided by 32 is 50, so there are around 50 teddies."

"There are about seven teddies visible on the top layer, and in the side view I counted around seven layers, so there must be about 50 teddies altogether."

"I can see about fourteen teddies in the side view. There are about four layers of teddies going back, so there must be around $14 \times 4 = 56$ teddies altogether."

"A teddy would fit in a 4cm by 4cm by 2cm space, which has a volume of 32 cubic centimetres. The jar is around 10 by 10 by 16 cm, which is 1600 cubic centimetres. 1600 divided by 32 is 50, so there are around 50 teddies."

Reveal that there are in fact 55 teddies in the jar and give students a few minutes to reflect on their estimations. You could reassure students that they are not expected to have got the answer exactly right and suggest that answers between 50 and 60 are reasonable estimates. Estimating from a photo is also quite tricky.

"The bottom of the jar is 10cm square, and the jar is filled to a height of 16cm.

If we wanted to design a jar that would hold 100 teddies, what dimensions could it have?"

Allow time for students to work in pairs, encouraging them to be prepared to share their reasoning, not just their answer, in due course.

In a mini plenary, invite students to share their ways of working and resulting answers. They are likely to have decided that, as there are approximately twice the number of bears now, a jar with twice the volume is needed. There is a variety of ways that this could be done. Watch out for the misconception that doubling all the dimensions will double the volume.

Show the picture of the larger teddy and share his dimensions: 16cm tall, 19cm wide and 12cm from front to back. Pose the question, "How would we work out how many teddies like this would fit inside our classroom?" (You may wish to divide this into the two subquestions "What do you need to know?" and "How will you work it out?".) Again, allow some time for thinking and discussion. This is an opportunity for estimating the classroom dimensions and perhaps some practical measuring. Once the dimensions are known, students put their plan into action to work out their estimate, perhaps using calculators.

In a final plenary, discuss the assumptions that have been made and whether they are likely to lead to an overestimate or an underestimate.

### Key questions

Can you use the ruler in the picture to work out any useful measurements?Does it help to work out the approximate volumes?

Can you tell me about your method?