This is a great lesson for all students, whether they love of math or struggle to stay afloat. It can be taught in the middle of the unit as review, but works great as an introduction, helping kids to place ratios into contexts they can relate to.
Lesson Plan:
1. hand out white boards to each student (*if you don’t already have a classroom set, order one! This is the most useful tool I have in the classroom to gauge understanding and to guarantee participation).
2. Show students an image of several animals (*mes-english.com has excellent handouts)
3. Ask students “How many of these animals have tails?” Allow them time to count, write an answer on their whiteboards and hold up their answer. Do not comment until all whiteboards are displayed. In this photo, all the animals have tails. Some debate may ensue, which is great! Once students have all agreed, write the ratio on the board, saying “So 15 out of 15 animals have tails.”
4. Next, ask students to write this as a ratio: 15:15. Ask them to explain what the “:” means: “out of” or “of”. It can also mean “compared to”, “related to” or “relative to.”
5. Quiz students again, this time asking which animals have humps/ wings/ paws/ feathers, etc.” Each time, ask students to write their answer as a ratio.
6. Next, hand out 3 smarties or skittles to each student. Ask them to write a ratio to represent the candy they have been given. Some students will write 1:3, 2:3 or 3:3. Others will write 1:2, 2:1.
7. Ask students how many smarties/skittles they have in total: 3. Ask them if, when they look at the ratio they have written, it gives a clue to someone else as to the “Secret language” you have written. In other words, math is a code language, have they written the code correctly? What does 1:3 mean? What does 2:1 mean? Do these ratios tell the same story?
8. What is the difference between a ratio and a pattern? For example, if I have 2:1 red:orange smarties, what would be the next in the pattern?
9. Tally each students smarty or skittles using the language “I have a ratio of one to three, red to pink“
10. Next, hand out a worksheet that shows ratios as they are represented pictorially (in nature). This worksheet asks students to count the leaves and then to count the trees and write a ratio. In other words, students are comparing parts vs. parts:
“For every 10 leaves, there are 3 threes. As a ratio this looks like 10:3.”
This next worksheet asks students to look at parts vs. whole:
“For every 8 beech leave I see, there are 2 oak leaves. As a ratio this looks like 8:2. I can simplify it further as 4:1.”
11. Ask students where it may be helpful to compare parts to parts, and where it is better to compare parts to whole.
- Ex. When cooking rice, there is a 1:2 ratio. For every cup of rice, add two cups of water. This is a parts to parts ratio.
- Ex. When you are watching a U10 soccer game, you notice that six players out of 11 can be on the field at one time. This is a ratio of 6:11.
12. Check in with students. Do they have any questions? Where have they used ratios in their own lives? How can they apply ratios to make life simpler?
13. Hand out a new worksheet. This time students are asked to convert pictures into numerical ratios:
14. Finally, students work with equivalent ratios worksheet:.
“This type of math is most commony used in cooking, when we double or half recipes. Where else is it used?”
Use word problems to quiz students understanding in follow up lesson. Once it is clear that they understand where ratios are used, the language that is used to describe ratios, and how to represent them pictorially or numerically, provide students with a visual that helps them understand that ratios and fractions are cousins/ best friends!
If you have lessons of your own that have helped students understand ratios, be sure to leave a comment below 🙂
Multiple Intelligences in the Everyday Classroom 