Algebra Tiles

Starting from a single piece of given information - that the little squares have a weight one unit - we are making discoveries about how we can determine the weight of the unknown blocks using only a balance scale.

Here is the page that we use for our visual.

Algebra Tiles

Here is what we did:

Using the small squares which weigh 1 unit - aka unit blocks - and the blocks of unknown weight, you are given a combination of blocks for each side which balances the scale.
You work to create a simpler situation without upsetting the balance.
Your goal is to simplify the situation enough so that everyone can easily see how much the unknown blocks weigh.

Here are the observations that you have made about the Algebra tiles that might turn out to be relevant to Algebra:

You can always remove the same amount of the same blocks from each side.

You want to have only unknowns on one side and only unit blocks on the other.

Using these observations, we determined that the green block must weigh 3 in this scenario by removing a yellow unit block from each side.

It does not matter which side has the unknown blocks.

If you divide each side into equal numbers of groups, a group from one side weighs the same as a group from the other side. Therefore, you can remove equal numbers of groups.

We determined that in this scenario, the green unknown blocks must weigh 2 units by dividing the green blocks into two groups, each with a single unknown block, and dividing the right side into two groups, each with two unit blocks.

You want to divide into groups so that there is a single unknown in each group.

You can rearrange and simplify the blocks on either side into groups without changing the balance.

By rearranging the blocks from what we were given (left) to how we want them (right) it doesn't affect the balance, but makes things easier to see.

Positive and negative values on the same side can be cancelled and removed.

You can add weight to the scale as long as you add the same amount on both sides.

Realizing that the red blocks are helium filled and lift up on the scale in exactly the opposite amount as the same-sized green and yellow blocks, we solved these scenarios.

Here are student-made stop-motion animations where they explain solving an equation.

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Algebra Tiles

Here are the observations that you have made about the Algebra tiles that *might* turn out to be relevant to Algebra:

Here are the observations that you have made about the Algebra tiles that might turn out to be relevant to Algebra: