Solving with Relational Rods

Today I was invited to see a lesson about solving equations using relational rods. This approach is new to me, and it was fun to learn alongside the students. Here we represent 20, and we know that when we split it into “m” pieces, the values of the pieces is 5. So we use 2 of the ten-rods to build 20, and we see that we need to split it up into groups of 5 (the light yellow is the 5 rod). There will be 4 groups, so m is 4.

Here’s another question: 4 groups of something equals 8. We know that the 8 rod is brown. We can use trial and error to find out what rods equal 8 when we use 4 of the same. The red rod works, and has a value of 2.

Here’s a more complicated one. 2 groups of something, minus 1, is equal to 5. That means 2 groups of something is one bigger than 5. 2 groups of something is equal to 6. The 5 rod (yellow) plus 1 (white) is equal to 6 (dark green). If we need to find a rod that can fit 2 into the space of the dark green, it’s the light green one, which is 3.

Here’s another: 2 groups of something, plus 6 equals 14. We build 14 from a 10 rod and 4 one rods (lots of other options we could have done). We know that 6 is a dark green. I need to now fill on the empty gap with 2 equal blocks. We can use the purple which is 4. Z=4

Here’s one last one, that was interesting….there were 2 ways to solve. The first way involved building 27. We used 2 ten rods and a seven rod. Then we used a 9 rod (blue) and had to fill on the gap with 2 equal sized pieces. Those pieces happen to also be 9s. We know a=9.

If we had built the 27 in a different way, we can see another property. We can build 27 as 3 nine rods (blue). Then we can build the 2a+9, so we put a 9 on top. We can see that on the top and bottom we have 9s, so those 9s are not needed…and can be eliminated. Now we just need to find 2 pieces that are equal to 18 total, which we can easily see are 9 and 9.

We followed this up with a bit of practice using algebra tiles to solve equations as well. It was a great learning experience for me.