##
* *Reflection: Intervention and Extension
Real-World Ratios Day 2 - Section 2: Real-World stations

Due to the ability level of my students this year, I chose to use only 3 of the questions to facilitate learning. We worked as a whole group. I read the questions to them and gave them the opportunity to solve on their own. I walked around the room and assisted the students that were having difficulty by asking them what the numbers mean (SMP2) and what tool would they like to use to solve.

Candies:

The problem that gave them the most trouble was the one where Valerie gave Cindy 1 candy for every 3 candies she eats herself. The students that used a ratio table came up with an answer of 4 candies because they used a 1 to 3 ratio to start. They knew that they had to get to a target of 12, but they misunderstood the numbers. The tape diagram worked best for this problem because students could see that each time 4 candies were eaten, therefore, Cindy got 3 pieces of candy and Valerie had 9 for a total of 12 pieces of candy eaten. If they wanted to use a ratio table, they would could start with the 1 to 3 ratio, but they would need to know that this still means that 4 candies were eaten all together. The labels would be Cindy to Valerie instead of Cindy to total. If they used the 1 to 4 ratio, they would find that Cindy got to have 3 pieces of Cany out of the 12 total.

Truffles.

The problem that gave the students the most trouble was the one that said they had plenty of cream and wanted to know how many truffles could be made with 8 cups of dark chocolate. The students wanted to know how much cream and I would say "plenty". So, I asked them what they already know. They said that they know that 1 cup of cream and 2 cups dark chocolate make 20 truflfles. I said "can we use this information to find out how many 8 cups of truffles makes?" Some students used the 1 to 2 ratio to start while others used the 2 to 20 ratio. It was cool to have them show these two strategies on the board. Most students used a ratio table to solve.

Escalator

I had to work through each problem with them. They struggled making the connection between the ratio given in the problem and then ones used for the answer. I showed them that we were trying to see if they could make equivalent ratios. I also explained that they could start with either ratio. Once we did a few problems together, they were able to start the other choices on their own.

Throughout these problems, I had the students talking to each other and working problems out on the board to help them verbalize and show what they know.

*Ratio Problems Reflection (Candies/Truffles/Escalator)*

*Intervention and Extension: Ratio Problems Reflection (Candies/Truffles/Escalator)*

# Real-World Ratios Day 2

Lesson 8 of 25

## Objective: SWBAT use multiple representations to solve real world ratio problems

*85 minutes*

#### DO NOW

*15 min*

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.

#### Resources

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#### Real-World stations

*60 min*

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.

*expand content*

#### Closure

*10 min*

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.

*expand content*

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- LESSON 1: Introducing Ratios!
- LESSON 2: Introducing Ratios - Stations
- LESSON 3: Writing Ratios the Right Way!
- LESSON 4: Writing Ratios the right way - Stations
- LESSON 5: Making Equivalent Ratios!
- LESSON 6: Equvalent Ratios Again!
- LESSON 7: Real-World Ratios Day 1
- LESSON 8: Real-World Ratios Day 2
- LESSON 9: Ratio Review for 6.RP.1, 6.RP.3a, 6.RP.3d
- LESSON 10: Ratio Assessment (6.RP.1,6.RP.3a,6.RP.3d)
- LESSON 11: Making the Most of Rates and Unit Rates!
- LESSON 12: Understanding Rates and Unit Rates Stations Activity
- LESSON 13: Using Rates
- LESSON 14: Are You a Good Consumer?
- LESSON 15: Using Rates Stations
- LESSON 16: Review of Rates and Unit Rates
- LESSON 17: Rates and Unit Rates Assessment
- LESSON 18: Scale Drawings
- LESSON 19: Constant Speed
- LESSON 20: Give me 100%.
- LESSON 21: Percents and double line diagrams and tape diagrams (Day 1)
- LESSON 22: Visually representing percent word problems (Day 2)
- LESSON 23: Solving Percent Problems (Day 1)
- LESSON 24: Solving Percent Problems (Day 2)
- LESSON 25: Performance Task (2 days)