Middle School Math - Exploring Ratios with Manipulatives

This activity is a great low floor, high ceiling hands-on math activity that takes zero prep and had all of my kids fully engaged.

My 6th graders this year love to use their hands and build. So, to help them better understand ratios, I decided to bring out the manipulatives.

First, I asked my students to find one or two partners, then in their groups select a collection of items from our manipulatives bins. I had tangrams, pattern blocks, beads, unifix cubes, cuisinaire rods, and place value blocks, but this could work with any manipulatives that you may have in your classroom.

When they had their items, I asked them to find as many ratios they could to describe relationships between their items.

For the collection above, they might find the following ratios.

triangles to hexagons = 7:3
unifix cubes to beads = 5:20
green triangles to triangles = 4:7
yellow to red = 9:3

I gave my students about 15 minutes to find and record as many ratio relationships as they could, in as many ways as possible. When they had found as many as they could, they then we went around to a few different groups to see if they could find even more ratio relationships.

Next, I challenged the students to build a design with their items with a green:yellow ratio of 6:4. Here are some of their designs.

Most groups chose to only use green and yellow items, but I was encouraged to see that a few used other colours, as well.

One group reduced the ratio to its simplest form of green:yellow 3:2 and created this design:

I loved that this activity allowed all of my students to participate at their own level. My struggling students were able to recognize relationships and record them as ratios in their collections, and still create a design with the given ratio. My proficient students were able to find a lot of relationships between the items in their collections, and were able to record part to whole ratios as fractions. My extending students were able to show the challenge 6:4 in different ways.

If you try something like this in your class, let me know how it goes in the comments below.

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