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Balance beam algebra

Balance beam algebra with ratios and substitutions

This math skill teaches how to balance equations using algebraic representations of shapes. The method involves multiplying or dividing both sides of the equation to maintain balance and using substitutions to simplify the equations, ultimately determining the relationship between different shapes.

Learn balance beam algebra

Teaching Transcript

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Let's solve the balance beam problem to find how many triangles would balance one circle

A balance beam is like an equation. If we keep both sides the same, it will balance. We can give a letter to each shape, and write out our equations.

Notice that we have two squares on the second balance beam. Let's double both sides of the first balance beam so we have two squares. Since we double both sides, it will still balance. Our equation also doubles.

We know that two squares is exactly the same weight as 6 triangles, so we can swap those out on both the balance beam and the equation. Everything still balances.

Now we have 3 circles balancing 9 triangles. If we line them up, you can see an interesting pattern. Every row is the same, so if three rows balance, then each row must balance

We can just pick a single row, which is the same as dividing both sides of our equation by three

So one circle is the same as 3 triangles.

Skill Practice

Balance beam algebra with ratios and substitutions

Test your understanding of balance beam algebra by practicing it! Work through the below exercises to use it in practice.