I’m going to have students answer the following question: Are all fractions ratios? Students should write their thinking down on a piece of paper or in their journal. The answer should include a reasonable explanation using mathematical terms. When students have completed their journaling, have them find a partner or two to discuss their answer. Offer this question up to the whole group to see if they made a connection that yes, all fractions are ratios, however, a fraction is written as a part to whole relationship and a ratio can be written part:part, whole to part, and part to whole.
The students will be rotating through 3 stations to reinforce their learning about writing ratios. Each station will last approximately 20 minutes and there will be approximately 8 heterogeneously grouped students in a group. The students will work with the teacher, at the computers and independently.
Teacher station: The students will be modeling ratios with the uni-fix cubes.(SMP 5) I’m going to try and get them to start reducing ratios or finding equivalent ratios. I have been making them say the ratio in a different way, but I haven’t used the words equivalent or simplifying. The students will be given several examples. I will want them to find the ratio in the problem, model, write it and then look at their model to see if they can make an equivalent ratio. By having the students move from a concrete representation to a mathematical representation, supports mathematical practice number 2. Some students may have a difficult time finding the equivalent ratio. I will be working with those students, using their manipulatives, to get them to see the equivalent ratio. For example, if there are 10 fingers on two hands, the students would represent this using the unifix cubes. Then I would ask them if there was a way to represent this by making equal groups for both comparisions: fingers and hands. Students should then see that there are 5 fingers for every 1 hand. Another example, if the ratio is 1:3, could we represent this another way. Students should see that there is no way to make equal groups. So ask the students if they can extend the ratio. What if we doubled the amounts, what would it look like? Is the ratio still the same?
Resource: unifix cubes and writing ratio worksheet
Independent Station: The students will be working on a worksheet that uses shapes to help them write the ratios and then simplify the ratios. If students finish early, they can check their work. I like to put a folder nearby with the answer key in it. This way students can check their answers and make corrections as needed. I may complete the first problem for them so they can see what a simplified ratio looks like. Then I will have them explain in words how I got that answer. Additionally, if students finish early, they can explain in words how they know what they know. (SMP 3) They can use the back of the worksheet to do this.
Resource: simple ratio worksheet (math-aid.com) and answer key.
Computers: The students will be visiting the following web site: http://www.thinkingblocks.com/tb_ratios/ratios.html Once the students are there, let them know they should watch the video before they begin to work independently. Students will be finding missing quantities. They will be representing the ratios with a tape diagram (previously used in their tool box) and using manipulatives to find the missing quantities. Students should have minimal difficulty with this as it is very visual.
Resource: computer with internet
I’m going to have the students use a model to show the solution to the following problem. They can do the work on a piece of paper which can be collected as evidence of student learning. Arielle drew a picture with a 1:4 ratio. Ben drew a ratio picture that had more than nine objects, but it was still a 1:4 ratio. Draw a picture to show what Stephan could have drawn. Explain in words the steps you took and why you took those steps