Equal parts

1.

Show the students a strip of paper. Use the names of two students in your class to create a sharing context.

• I will share this strip between [Name] and [Name].
• How many pieces do I need?
• What is the size of each piece? (Tell students the pieces are called halves)

2.

Cut the strip unequally and give a piece to each of the two students.

• There we go. I gave one half to each student. They should be happy.

Look for students to say that the sharing has not been fair because one person has a greater share than the other. If this idea is not offered, discuss what it means for shares and situations to be fair. Use contexts that are relevant to your students.

• How can I check that the pieces are the same size?

Look for students to suggest that aligning the strips in some way is a good way to check for equality.

3.

Establish the idea that for fractions to be correct, the parts must be equal.

• The pieces I gave [Name] and [Name] were not halves. The pieces were not equal – they were not the same size.
• Can you help me make halves?

Introduce relevant teo reo Māori kupu as relevant (e.g., ōrite - equal, ōrite-kore - unequal).

4.

Lay another strip on the floor or tabletop.

• I need you to put your hand up when you think I should stop, then cut the strip.

Slowly move the scissors across the strip from left to right. Students should raise their hands at approximately the half-way mark. Draw a vertical line at the half-way mark when students determine it.

• Does that look right? If I cut here, will I have halves?

Students might argue that it looks right because the same amount of strip is on either side. Some might suggest using a ruler to check.

5.

Cut the strip and give a piece each to the two students. Check the equality of the pieces by aligning them.

6.

Do the same thing, sharing a strip among three, four, and five students, to create quarters, thirds, and then fifths. Increase the difficulty of the task by asking students to compete to say "stop" at the right points as you move the scissors across the paper. Introduce relevant teo reo Māori kupu as relevant (e.g., haurua - half, hautoru - third, hauwhā - quarter, haurima - fifth).

7.

Write the words "equal" and "unequal" on the board. Display the examples of equally and unequally partitioned strips next to the labels.

8.

Provide students with the Equal parts CM. Let them work independently, or in pairs, to determine whether or not each strip is cut into equal parts, and circle the word that applies to each example, equal or unequal. Watch as students work and look for them to do the following:

• Use symmetry for halves, quarters, and eighths.
• Use direct measurement, such as creating a measure of the first part and iterating it across the strip, to decide whether the partitions are equal.
• Name the fraction part.

9.

After a suitable amount of time, gather the students to discuss their strategies and answers. Pay particular attention to the use of symmetry and measurement to determine whether or not the parts are equal.

1.

Work on students’ fluency in naming the fraction parts. Students should be able to name halves, thirds, quarters, and fifths, then extend naming to fractions where the language code is clearer. For example, tenths mean ten equal parts.

2.

Work from part to whole. Give students a length and call it a fraction name; say:

• This is one quarter. How long is the whole (one) strip?

Change the unit fraction you name and the size of the part. Look for students to create a whole from the given part.