SWBAT use multiple representations to solve real world ratio problems

Using rich math problems and multiple representations to solve ratios.

15 minutes

I’m going to have them read an article about a chef who uses ratio to develop his recipes. I want the students to read the article and choose a ratio to create their own problem and represent it visually to show how to get to the answer. Students may use tables, graphs, double line graphs, tape diagrams, or equivalent fractions. This article is a real world connection to ratios.

60 minutes

I’m going to have each table set up with a rich mathematical problem which will require some thinking and understanding of ratios. The problems will be set up to be semi-challenging to challenging. I’m going to stay close to the challenging problems to help assist with their learning. I’m going to have 8 problems for the stations. If you need more problems you can visit www.insidemathematics.org or www.illustrativemath.org. Both are good websites to get some decent problems. The problems for today came primarily from these sites.

Each group will be allowed to work on a problem for 10 to 15 minutes depending on how many groups you have. Tablemates will be their group members for today. Groups will then be mixed by ability so there can be some peer tutoring if needed. It really isn’t necessary to get groups to work out all the problems. More importantly, we want the students to deepen their understanding of ratios, make connections to real life, and use multiple representations to solve the problems. Each station should have enough copies for the students to look at on their own (4 or 5)

Problem 1: Heart beats

The students will be calculating out how many times their heart beats in a month. This station will need a stop watch. Students will need to figure out how many times their heart beats in a minute and then calculate how many times in a month **(SMP 5: tools)**

Problem 2: Candies

The students will be making connections between fractions and ratios in this problem. It is a multi-step problem. This is a grade 5 problem, but connects nicely to our learning. I'm not anticipating any struggles with this problem.

Problem 3: Truffles

This problem has them doing ratio calculations with real world material. The students will also need to use a graph to come up with a solution.

Problem 4: The Escalator

The students will apply their knowledge of ratios to figure out which of the solutions will work.

Tell students there are some non solutions choices.

Problem 5: Jim and Jesse’s money

The students will be using a visual representation (tape diagram) to help them find out how much money they started out with.

Problem 6: Mixing Concrete

The students will be using a visual representation to help them find the solution to this ratio problem. Tape diagrams or ratio tables will work best. Students may not realize that both sand and cement need to be added together to get the total volume.

Tape diagram: 5 parts sand to 3 parts cement makes 8 parts total. 160/8 = 20 parts needed for each

5 x 20 = 100

3 x 20 = 60

This makes a total of 160 parts

Problem 7: 2 Random problems.

There are two real world ratio problems on the page. For this problem, I would make a copy for each student because they will be graphing their ratios on the coordinate plane. You can collect this problem for evidence of student learning. Students will need to make a ratio table to keep track of their results. Make sure they label their ratio table. (**SMP 6)**

Problem 8: Comparing Heartbeats

This problem has the students finding out what the difference between an out of shape heart beat and an in shape heart beat. This problem may give students a difficult time. The solution shown is a visual of dimensional analysis. We are not expecting the students to solve it that way. So to get students started, I would ask them to calculate a regulary heart beat per hour. They can set up a ratio table to do that. Then, I will ask them to calculate how many times it will beat in a day (24 hours). Since this is for a regular heart beat, the problem states that an out of shape heart beats 20 times more. Students can then multiply their solutions by 20.

10 minutes

Ask the students to take a moment and think about which strategy makes the most sense to them when solving ratio problems? Explain why this strategy is the best one for you. Have students journal about this in their spirals or on the page in their tool box.