Learning With Fractions...

Problem of The Day

Can You…

Can you fold a piece of paper in half more than 7 times?

Do you need to change the shape?

Would using different paper help?

Comparing Fractions

Cut 10 strips of paper, 10cm long, 1-2 cm wide.

Fold one strip in half, one in quarters and one in eighths. Draw in the fold lines.

Now do the same to make a strip with 3 equal parts (3rds) 6ths and 9ths.

Now try 7ths.

Finally, make one with 5ths, and then 10ths.

Now put them in order, 1 whole – tenths. You have made your own Fraction Wall!!

Rather than measure these sections, the focus is to fold them. What strategies did you use? How did you go with the odd numbers?

(The focus here is on the kids actually creating their own fraction wall, rather than just colouring in one that is already produced for them. They see the transition from a whole to the fractional parts, and the equality of the divisions. They also see the relationship between halves, quarters and eighths etc. The next few activities with fractions can be done using this wall as a resource)

Halves and Quarters

Choose two or more of these shapes (or all!!)

Triangle, Square, Rectangle, Circle, Diamond, Pentagon, Hexagon, Octagon

Draw it.

How many different ways can you divide each shape into halves and quarters?

Are two quarters always the same shape as a half?

Equivalent Fractions

Mia was offered 1/3 of a pizza by Sam, and then Jane came and offered her 2/5 of her pizza.

As she was pretty hungry, which offer was the best?

Use your fraction wall to help.

OR… Draw 2 circles. Divide one into 3rds, the other into 5ths. Use this model to decide.

What other fractions are the same, even though one might have more pieces? Eg Compare 2/3 and 4/6, 2/5 and 4/10

What patterns in the numbers do you see?

Are Fractions always equal?

Dan announced “Three quarters equals six eighths”.

Milly replied, “Not always, it depends!!”

Can you explore how both children can be right?

Can you draw your response to this to show how they can both be right?

(We are trying to draw out the idea that for ¾ to be equal to 6/8, the wholes must be the same. If I had ¾ of a small pie, and someone else had 6/8 of a much larger pie, they are clearly getting more, because the wholes that we are comparing are not the same)

Fraction Tapes

Start with four 10cm lengths of paper. Each one is a whole. Label them in halves.

Join them end to end to make up some equations that add up to 4. Eg 1 ½ + 2 ½ = 4

Use improper fractions 3/2 + 3/2 + 1 = 4

Make tapes for 3rds, quarters, sixths and eighths.

Combine fractions that add up to 4.

What tapes can you use to show 2 ½ ?

If I added 1/3 to 1 ½, what would this show?

Sharing in a Group

If I share 3 Cherry Ripes between 4 people, show how much will each person will get. In a number sentence we would write

3 ÷ 4 = We have more people than Cherry Ripes, so they will not get a whole one each. They will get less than a whole Cherry Ripe.

Eg (These are multi coloured Cherry Ripes!!)

Red gets ¼ of each bar, which makes ¾ all up

The same for the other 3 people. Everyone gets ¾

Use this method to show…

2 ÷ 3 = 4 ÷ 6= 3 ÷ 5 =

Rolling Dice

Use 2 of the dice you have at home (Do you have 6 sided?)

Or, you could make your own dice from a paper cube, similar to the ones you may have made in class at some stage.

There’s another maths activity to refresh yourselves with!!!

On little bits of paper, paste these numbers on each side.

Dice 1 – 1/4, 2/6, 4/5, 1/6, 2/3, 6/10

Dice 2 – 1/3, 2/12, 3/5, 8/10, 4/6, 2/8

Take turns rolling the dice. Decide whether the fractions are equal or not. Give reasons for your decisions.

Fraction Problem

I heard two students discussing fractions.

One said “2/14 is double 1/7”.

The other student disagreed with him, and said that they were the same size.

They came to Me to sort this out and to see who was right.

Can you draw a diagram to explain who is right, and explain it?