Fraction Uncover

Curriculum Goal

Junior: Number Sense

Represent equivalent fractions from halves to twelfths, including improper fractions and mixed numbers, using appropriate tools, in various contexts.
Use equivalent fractions to simplify fractions, when appropriate, in various contexts.

Fraction Goals

Fraction Equivalence
Fraction Magnitude

Lesson

Children match equivalent fractions using a fraction area model.
The objective is to remove all tiles and uncover the grid.
Each child is assigned a 4x4 game board. They begin by covering the entire board with 1/16 pieces. Next, they layer 1/8 pieces on top, followed by 1/4 pieces, and finally place the 1/2 pieces on top.
One at a time, each child draws a fraction card from the deck of cards. Then, they choose one of three actions:
1. Remove one or more tiles from their grid that are equivalent to the fraction on their card. The number of tiles being removed MUST be equivalent to the fraction card they pulled.
- a. E.g., if the child draws the 1/2 card, they can remove any combination of tiles on their grid that is equivalent to 1/2 (e.g., two 1/4 tiles).
- b. E.g., If a child draws the 1/2 card and only has one 1/4 tile left on their grid, they will not be able to remove. They can only exchange or do nothing.
- c. However, if they have one 1/4 tile and two 1/8 tiles on their board, they will be able to remove them when they draw the 1/2 card.
2. Exchange any of the tiles on their grid for equivalent pieces.
- a. E.g., exchange the 1/2 tile for two 1/4 tiles.
3. Do nothing.
- a. E.g., if the child draws the 1/4 card but only has one 1/16 tile left on their grid, they must skip their turn.
Remember children can only perform one action per turn. They cannot remove and exchange on the same turn.
The first child to remove all the tiles and uncover their grid is the winner and gets one point.

Look Fors

What strategies do children implement when choosing tiles to exchange on their grid? Do children choose a combination of tiles or primarily one type of tile?
How do children explain the concept of fraction equivalence using the area model when removing equivalent fractions from their grid (e.g., “two 1/16 tiles take up the same area as the 1/8 tile, so 2/16 is the same as 1/8”)?

Instructional Script

Step 1

We are going to play a game called “Fraction Uncover”. [screenshare the instructional slideshow]

[next slide]

Everyone will be assigned a fraction grid.

Before we start the game, you are going to cover your grid with two 1/2 tiles. The goal of the game is to remove all the tiles and uncover the grid below — the winner is the first person to uncover their grid!

[next slide]

You will take turns drawing fraction cards from the deck. Once you’ve drawn a card, you can do one of three actions: remove, exchange or do nothing.

[next slide]

You can remove a fraction tile that matches the fraction on your card. For example, you can see that I have two 1/2 tiles on my grid at the beginning of the game. If I draw a 1/2 fraction card, I can choose to remove one 1/2 tile from my grid. [next slide]
You can exchange one of your fraction tiles for different fraction tiles. Let’s say I draw a 1/4 fraction card instead. I can’t remove anything from my board because I only have two 1/2 tiles, but I can exchange one of my 1/2 tiles for one 1/4 tile and two 1/8 tile. [next slide]
You can do nothing. If I can’t remove or exchange any tiles, then I can’t do anything but wait for my next turn.

But remember, you can only do one of these three actions — you can’t exchange fraction tiles and remove them in the same turn.

[next slide]

Step 2

Example 1:

Let’s try an example! I got the 1/2 fraction card.

Since the point of the game is to uncover the grid, I want to try and remove any tiles first. Can I remove any tiles from my grid? [class answers yes, the 1/2 tile]

[next slide]

It looks like I can remove the 1/2 tile from the grid!

[next slide]

Example 2:

[slide 9]

Let’s try another example. Here we have a 1/4 card.

Do any of the tiles match the 1/4 fraction card? Remember, we need to remove equivalent fractions from the board, not more or less! Maybe I can exchange one of the tiles instead to prepare for future turns.

[next slide]

Since we could not remove exactly 1/4, we exchanged the 1/2 tile for one 1/4 tile, one 1/8 tile, and two 1/16 tiles.

Step 3

Does anyone have any questions? [pause for children to ask questions]

Perfect, let’s get started! [share link]

Specific Scenarios

Example 1: Child picks up 1/4 fraction card but only has three 1/16 tiles on their grid.

Child: “I think I can remove all my tiles and win the game now.”

Instructor: “Let’s compare the size of the 1/4 tile to the three 1/16 tiles. What do you notice? Do they take up the same amount of space on the grid? How many 1/16 tiles make up the 1/4 tile on the grid?” (encourage children to use the visual tools)

Child: “No, the three 1/16 tiles take up less space on the grid. I need four 1/16 tiles to make up the 1/4 tile.”

Instructor: “Okay, so that means that 1/4 is not equivalent to 3/16. You’ll need to wait until you pick up a fraction card that is smaller than 1/4 to remove tiles from your grid.”

Example 2: Child picks up the 1/16 card but only has 1/2 and 1/4 tiles on their grid.

Child: “Can I remove my smallest tile from my grid?”

Instructor: “Remember, we can only remove equivalent fractions from our grids. What does the 1/16 tile look like? Is it the same size as the 1/2 or 1/4 tiles? Compare the tiles side by side.”

Child: “The 1/16 tile is a lot smaller than the tiles I have on my grid.”

Instructor: “Exactly. That means there isn’t an exact match on your grid. What tiles could you exchange to be prepared for your next turn?”

Example 3: Child picks up the 1/4 card with two 1/8 tiles on their grid.

Child: “I picked up 1/4 but I don’t think I can remove anything from my grid because I don’t have any 1/4 tiles.”

Instructor: “Okay. Can you put any tiles together to make the equivalent of 1/4? It looks like you have two 1/8 tiles on your grid. Let's compare the size of the two 1/8 tiles to the size of the 1/4 tile! What do you notice?”

Child: “They look like they’re the same size.”

Instructor: “Yes, the 1/4 tile takes up the same amount of space on the grid as two 1/8 tiles. That tells us that one 1/4 tile is equivalent to two 1/8 tiles. In other words, 1/4 is the same as 2/8, because they are equivalent fractions!”

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