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Level Two > Number and Algebra

# Wafers

Keywords:
Achievement Objectives:

Specific Learning Outcomes:

Find unit fractions of regions.

Description of mathematics:

Number Framework Stage 5

Required Resource Materials:
Wafer biscuits (rectangles made from grid paper can be used).
Activity:

#### Background maths

The students must realise that the symbols for fractions tell how many parts the whole has been divided into (the bottom number or denominator) and how many of those parts have been chosen (the top number or numerator). For example, 2/3 shows that one (a whole) is divided into three equal parts (thirds) and that two of those parts are chosen. Note that the terminology is not as significant as the idea, although the students will acquire the correct terms if they are used consistently.
Students also need to appreciate that the most common context for fractions is division where the numbers do not divide evenly. For example, when four people share 14 things, each person will get three things but two things will remain to be shared. These two things must be divided into halves to make the equal sharing possible.
The English language presents a barrier to the students generalising the meaning of fractions. Halves, thirds, and quarters (fourths) are special words, and it is not until fifths (five-ths), sixths, sevenths, etc. are encountered that the “ths” code becomes evident.

#### Using Materials

Problem: “I want you to work in pairs. You will get three wafer biscuits. Think about how you might share the wafers so that each person gets half of the wafers.”
Tell the students to discuss how they will cut up the wafers so that they can be shared equally. Some students will suggest cutting each wafer in half, but others will suggest giving each person a wafer and halving the remaining one. Discuss how these methods compare, that is, three halves make one and one-half wafers.
Ask, “How can we check that each person will get the same number of wafers?”
The wafers can be cut and each person’s share of wafers put end on end. Ask the students how many wafers each person is getting.
Develop vocabulary like “one and one-half” and “three halves”. Use symbols to record their findings:

Generalise the ideas further with similar problems, like:
“This time you will be in groups of four, but I will still give you three wafers. Find a way to share the wafers equally.  How much wafer will each person get?”
Ask the students to predict how much they will get.
“It will be less than a whole wafer because four people would need four wafers for that.”
“We cut each wafer into four pieces Each person gets three pieces. What are the pieces called?” (quarters)
Provide other examples for exploration with the materials, such as:
Three people share four wafers. Four people share six wafers.

#### Using Imaging

Third Person: Pose this problem: “Suppose there were three people, and they had to share two wafers. How much would each person get? I want you to think about that and draw a picture to show your ideas.”
Discuss the diagrams the students draw using the language of fractions.

“You have cut each wafer into three pieces. What could you call each piece?” (one third)
“How many of those pieces will each person get?”
If the students do not have the language of thirds, tell them about it.
For example, “One-third and another one-third is called two-thirds.”
Record the students’ findings using symbols.
For example, 1/3 + 1/3 = 2/3.
Pose other similar problems to see if the students can image a way to anticipate the sharing of biscuits.
“There are five people at the party and six wafers. How much wafer will each person get?”

#### Using Number Properties

The students have a good understanding of equal sharing when they can anticipate theresult using the properties of the numbers involved rather than relying on images. The number size is increased to promote generalisation.

“Suppose I put you in groups of six people. Each group would get four biscuits. How much biscuit would each person get?”
Look for responses like:
“They will get more than one-half but less than one.”
“How do you know?”
“It takes three biscuits to give each person one-half, but to give them each one whole biscuit would take six.”
“That would be the same as three people sharing two biscuits.

## Fractional Blocks

Find fractions of regions.

## Fractional Blocks

Find fractions of regions.

## Fraction Circles

Order fractions with the same denominator.

## Fair Shares

Find halves and quarters of sets, regions and objects by sharing.

Find simple fractions of regions.

Find fractions of sets by sharing.

## Dividing Fractions

learning how to divide a fraction by a fraction