# Matching Cards

### Task 12 ... Years K - 6

#### Summary

The initial challenge for each is to correctly match pieces, then to order the correct matches. But how many not-matches are possible?

Designed as an example of what a task card for Infants (Years K - 2) might look like, the task illustrates:

• a challenge involving age-relevant content,
• minimum use of written language,
• support for language development through repeated sentences and vocabulary,
The task can be simplified as necessary by using two rather than three pictures and by removing one or more of the matching pairs for each picture.

#### Materials

Three pictures (teacup, beach ball, carrot), each in 4 sizes and each cut into 2 parts. Therefore 8 pieces for each picture and 24 pieces altogether.

#### Content

• recognition of attributes of objects
• recognition of left and right sides
• sorting, classifying, ordering
• recording data
• informal experience with probability

#### Iceberg

A task is the tip of a learning iceberg. There is always more to a task than is recorded on the card.

1. For each picture, how many not-matches can we make? How can we record them?
2. If you put the 8 teacup pieces into a bag and choose two pieces without looking, do they match? How many times do you have to repeat this experiment (replacing the pieces after each try) before you make a match?
3. What happens if your friend tries the same experiment? How many times before they make a match?
4. What happens if you use the pieces of a different picture? Does it still take about the same number of tries to make a match?
5. Display a record of how many tries it takes with the teacup pieces for each person in the class to make a match. Is there a pattern?
6. (For older students ... and their teachers): Calculate the probability of making a match playing the 'bag' game with 8 teacup pieces.
7. (For older students ... and their teachers): Suppose each of the 4 sizes of carrot picture was cut into three parts, making 12 pieces altogether. What is the probability of a match if you play the 'bag game' by choosing three pieces without looking?
A New Thought
Teresia Brzokoupil, a teacher at Trädgårdsstadsskolan, Tullinge, near Stockholm, has suggested an iceberg question using these cards:
• Look at the teacups. The size of the outside card is always the same. It is the size of the teacup frame which changes. Can you calculate the scale factor used to make each smaller teacup from the largest one?
• Have the same scale factors been used for the carrots and beachballs?
Another New Thought
Clare Malone, Alsager School, Cheshire, UK asked the question:
• If the carrots are all the same size, how far away are they?
Her colleagues in the workshop really liked the question. Try it and let us know how your students respond.

Other Thoughts

• Spread out the full set (or a subset) of the cards face down and play Memory to make a match.
• If instead you play the game Go Fish students have to ask for the card they need to complete a match by describing it, eg: left side of the second smallest teacup.
• Capitalise on the students interest in doing the matching by introducing a time challenge to complete the matches and make the grid below.
• Arrange the cards in an array of matches as below. Try fraction-based challenges like:
• What fraction of the cards are the smallest?
• What fraction of the cards are balls?

#### Whole Class Investigation

Tasks are an invitation for two students to work like a mathematician. Tasks can also be modified to become whole class investigations which model how a mathematician works.

The 24 pieces in this task are sufficient in themselves to create a whole class lesson with most infant classes. Hand out one piece to each child and ask them to move around and find their match. When the matches are made place the matched pieces on the floor and sit in a circle around them all. Ask particular students to find:

• The largest teacup.
• The smallest ball.
• The second biggest carrot.
and so on. Also choose students to arrange the matched pieces in order. From here any of the challenges in the iceberg section above can be explored as appropriate to highlight aspects of the work of a mathematician.

To relate the task to other familiar infant activities such as the story of the three bears with their three sizes of bed and so on, you could remove one matching pair from each picture set, leaving 18 pieces altogether.

#### Is it in Maths With Attitude?

Maths With Attitude is a set of hands-on learning kits available from Years 3-10 which structure the use of tasks and whole class investigations into a week by week planner.

Matching Cards is not in any MWA kit. However it can be used to enrich the Space & Logic kit at Years 3/4 or Chance & Measurement kit at Years 9/10.

Also Task 224, Matching Faces, has similarities and Matching Faces is an integral part of:

• MWA Chance & Measurement Years 5 & 6
• MWA Chance & Measurement Years 7 & 8