How Do You See It?
1 out of 3
Here are some short problems for you to try. Talk to your friends about how you work them out.
Problem
How Do You See It? printable sheet
Here are some questions.
How would you represent them using:
- pictures?
- numbers?
- objects?
Can you think of any other ways of representing them?
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| Zoe had three sweets. Her friend Ranjeet gave her two more. How many sweets does Zoe have now? |
Karala had 8 teddies. She gave 3 of them to her little brother. How many teddies has Karala got now? | Image
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It was Toby's birthday and he had 6 birthday cards. Some more cards arrived in the post and then Toby had 9 cards. How many cards arrived in the post?
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Si had eight balloons. Some popped and he only had five left. How many popped?
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| Some children were walking to school. Three more children joined them. Then there were nine children altogether. How many were walking together at the beginning? |
Marcus had some coins in his pocket. Sadly he lost seven of them and now he only has three coins. How many coins did he have before he lost some?
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Getting Started
Find some Lego figures and toys or objects such as counters to make sense of the problem.
Student Solutions
We had a number of solutions sent in that provided the "answers" to the calculations. Voltaire from Ravenor Primary School in England sent in the calculations explanation as follows:
$1.5$ doing $3+2=5$, $2.5$ doing $8-3=5$ $3.3$ doing $9-6=3$,
$4.3$ doing $8-5=3$, $5.6$ doing $9-3=6$, $6.10$ doing $3+7=10$
Our first contribution to the Primary site, not in English came from Jose at the Esapana Istituto;
Esto es para dos de los problemas. Mi hermana pequeña, Anya ellos lo hicieron por mÃ. Ella tiene cinco años.
Zoe tiene 3 caramelos. Rajneeti le da dos más. 3 +2 = 5 / tres y dos son cinco
Karala tena 8 muñecas.
Ella le dio tres de ellos a su hermana pequeña. ¿Cómo ha Karala muchas muñecas tiene ahora?
As que 8-3 = 5 / ocho menos tres es igual a cinco
Which I think says:
This is for two problems. My little sister, Anya they did for me. She is five years.
Zoe has $3$ candies. Rajneeti gives you two more. $3 +2 = 5$ / three and two are
five
Kerala had $8$ dolls.
She gave three of them to his little sister. How many has Karala
dolls have now?
So $8-3 = 5$ / eight minus three is equal to five
Thank you Jose, for that. Thanks also to Voltaire
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This activity encourages children to think of different ways of viewing the calculation. Whilst they are doing this the teacher can observe just how their pupils are considering a problem, and this may be somewhat different from the taught approach. Given the opportunity, children often have their own ways of working.
Possible approach
Talk to the children about how different people do things in different ways and explain that this actvity is all about that - it's important that the children don't presume that there is one way and one way only to see the calculation.
Working within a pair or small group and tackling one problem at a time can help children to focus more deeply on one task rather than racing through them. You could suggest that they think and talk about what they are going to do before they actually begin.
They may decide to enact with objects or make a picture and just record the answer. Or use these as a prompt to transfer the problem to a calculation which they would record horizontally. Whichever, your observations will allow you to reflect on the children's confidence, language and understanding and possibly what misconceptions they hold.
These particular examples are reasonably straight forward. 'How many more than..?' type questions are much more difficult because the word 'more' usually signifies addition but the calculation here is a subtraction. It's worth introducing word problems in this category separately by taking a lesson to focus on them.
There are eight types of change and compare word problems. You might like to look at more examples of word problems, including ones that children typically find difficult. You can read more about this in: Harriett C. Bebout, (1990) Children's Symbolic Representation of Addition and Subtraction Word Problems, Journal for Research in Mathematics Education, Vol. 21, No. 2, pp. 123- 131, NCTM
Key questions
Tell me how you are working this out.
What do you think of _____'s way of doing this?
How did you know what to do first?
Is the way you've done this differently from the way you do other additions/subtractions?
Possible extension
Ask the pupils to create stories that involve calculations for their partners to do.
Give the pupils a written form of an addition/subtraction e.g. [] - 5 = 12 and challenge them to create a story around it.
Possible support
Some pupils will benefit from working with some small toys/dolls so that they can enact the situation before being able to think about the calculation, for example the final balloon problem might be modelled using Lego figures and counters as the balloons. The physical act of moving objects in different ways (together, away from) can sometimes help less confident children to work out which operation is appropriate.