Simple Picture or Mathematics? CCSSM6.R.P.1.

The picture above may look simple, but it is filled with math concepts. For this picture, students will be using a handout, like the one provided, to find ratios. In this picture, students will first be asked to look at the picture for about 5-10 seconds and record their guess of whether there are more circles or triangles in the picture. After making their guess, students will be asked to count the number of circles in the picture, and the number of triangles. Look closely! After finding both of those numbers, students will find the total, and then be asked to find certain ratios between the shapes. They can also be asked to explain what the ratios mean to help extend their thinking. This activity aligns with CCSSM 6.R.P.1.

Picture Blog Assignment

Fashion Drawing vs. Real Humans CCSS.MATH.8.F.B.4 & 5, MP4

Blog Image

This is an 8th grade modeling lesson aligned with linear function models and graphs. Are the fashion artist’s proportions right? This activity challenges students to analyze body proportions generated by a fashion illustrator, then compare them to the student’s own specific body proportions. Students will collect data into a table, plot it onto a graph, and generate an equation to determine the accuracy of the fashion illustration’s proportions.

 

Fashion Proportion vs Human Proportion

Picture Problem: Potato Chips

o-CRISPS-570 p0376182 potato-chip-taste-test_612

 

People are often frustrated with the amount of chips that come in a bag of chips. Or lack thereof.

For this activity, students will find out the average amount of chips found in bags of chips. They will then find the average size of a chip, and the amount of space that a chip bag can hold. From there, they will figure out how many chips could fit in bags if companies filled them up, and compare that to how many they actually put in the bag.

Example: Lays potato chips. Out of x amount of bags, they hold an average of y amount of chips, filling z% of the bag. Therefore, if they filled the bag, they could fit a amount of chips.

 

They could complete this through proportions

CCSS.MATH.CONTENT.7.RP.A.3
Use proportional relationships to solve multistep ratio and percent problems.

or geometry, using surface area and volume

CCSS.MATH.CONTENT.7.G.B.6
Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms.

M&M’s

M&M’s

 

P

All middle school students love M&M’s! All middle school students love engaging lessons. Why not combine them to make a lesson your students will never forget?

Ask your students the big, important question at the beginning so they know what they’re focusing on: How many M&M’s will fit in a gallon jug? Have the students discuss the question for a few minutes with their classmates, then have each student guess how many will fit in the jug. Depending on your classroom, you could have them right their guesses on a piece of paper or on the whiteboard.

Students will get into pairs and each group will fill a graduated cylinder with 50mL of water, then add 10 M&M’s into the graduated cylinder. After a quick calculation, they will find out how many mL are “equivalent” to 10 M&M’s. Students will need to convert mL to gallons, then mathematically find out how many M&M’s will fit into a gallon jug.

Have each group add their M&M’s into the empty jug. The students can count and continue to add them into the jug making sure to keep track how many are in there. Once the jug is full, the class will find their answer. As a class, compare this number to their guesses to see who was the closest.

CCSS.MATH.CONTENT.6.RP.A.3.D
Use ratio reasoning to convert measurement units; manipulate and transform units appropriately when multiplying or dividing quantities.

Super Bear 6.RP.A.3

How many regular size gummy bears would it take to equal one Super Bear? How about mini bears?

super bear

Students explore concepts of proportions and rates as they determine the relationships between three different sizes of gummy bears. The lesson uses a series of short multimedia videos that provide small amounts of information in a real-world problem to create intrigue. Specifically, the first video shows someone placing three different sizes of gummy bears on a table: a “mini” bear, a “regular” bear, and a “super” bear. The video ends with the three bears aligned in a row, without posing a question or providing information. The video inspires students to solve a problem by formulating their own instinctive questions and seeking out missing information.

Throughout the lesson, students guide their own learning by deciding how to solve the problem and what information they will need to do so. Working in groups, students will arrive at a solution and then share their process with the rest of the class. Students may be given guiding questions or ideas if they seem lost, but the lesson should rely on students’ abilities to discover and problem solve within groups. Once each group has shared their own ways of solving the problem, the teacher will show the whole class a new method for finding the answer using ratios and proportions. The lesson provides several opportunities for extension, including solving for both mini and regular size bears, as well as determining which option of bear provides the most gummy for the least amount of money. The lesson meets CCSS.MATH.CONTENT.6.RP.A.3, MP.1, and MP.4 in the Common Core State Standards.

super bear2

Find the videos for the lesson here.

Follow our lesson plan here: Super Bear Modeling Lesson

By Brittany Stevens, Devyn Hunter, Kelly Yingling, and Enrique Gudino

How Tall is That? 6.RP.A.3

MATH VisualCan’t measure the height of that tree with your ruler? No problem! Let’s use ratio’s to find it’s height!

This lesson is a great modeling activity where students are able to apply ratios and proportions to real world situations. They will be using the concept illustrated above with objects they find around their school. The students will find their own height and shadow length, and use this ratio to find the heights of several tall objects. Some of these might be basketball hoops, portables, school buildings, soccer goals, railings, and even the height of their own teacher! Continue reading

7-RP Learning Progression for ratio and proportional relationship with real world applications

Pizza
unit_rate
Attached is a learning progression about the ratio and proportional relationship CCSS.MATH.CONTENT.7.R.P. students expand upon their previous knowledge about ratios and develop an understanding of proportional relationships. Students use ratios to represent real world scenarios and compute unit rates in order to compare ratios with the same units. They use equations to represent and analyze proportional relationships. They also must be able to graphically represent proportional relationships and explain what each coordinate on the graph represents in terms of the scenario. Students will also have to solve multi-step ratio and percent problems. By the end of this unit students will be able to solve problems involving discounts, taxes, percentage increase and decrease, and use scale models. Throughout the learning progression there are multiple mathematical practices and visual representations to aid students with learning disabilities and different learning styles to help them achieve mathematical understanding regarding ratios and proportions.

Along with the learning progression is an kinesthetic activity that engages students in practical applications of unit rates. The problem, “A pizza with 8 slices evenly proportioned cost $14.80, what is the cost of each slice of pizza?” Will be used as the real-world situation to find the unit rate, make a table and graph to represent the data, and as information for an equation to represent the proportional relationship. Each student will make their own pizza with 8 slices evenly proportioned. Students will need to remember unit rate definition to find the unit rate and write the unit rate on each slice of pizza. Using Geogebra students will be asked to make a table and graph to represent their data. Students will be formatively assessed throughout the lesson to provide evidence to provide feedback about whether students are ready or not for the benchmark assessment that will be given the following day testing the standards gone over in this lesson. Students order pizzas and other take out food, so being able to solve this problem will be useful for them to figure out how to save money and get the better deal when ordering food. If some students do not like pizza you could give them a different type of food to peak all students interests and make it relatable to them and increase the diversity of curriculum in the classroom.
LP and lesson plan

6.RP.3 Coke v. Sprite 3- Acts Math Task

To help students be engaged in the classroom, it is important for teachers to capture the students’ attention and relate material to the students. This will create more interest and hopefully will result into more learning taking place in the classroom. Most students like to drink soda, so involving something they may like with ratios and proportions can enable students to grasp the concept a little easier.

The Coke v. Sprite math problem was found on the Dan Meyer’s 3-Act Math task website. This problem has students think about ratios and proportions in a different way, while mixing two sodas and figuring out which soda contains more of its original soda. This activity can be found at the following link: http://mrmeyer.com/threeacts/cokevsprite/

sprite and coke

To begin the lesson, the teacher would pose the question by showing the clip and asingk students to make individual guesses with a written reason of why he or she responded the way they did. The students’ reasons are very important. The teacher should encourage students to use pictures, symbols, or anything that will be helpful when explaining his or her reasoning to somebody else. After allowing students enough time to think about their reasoning and write it down the teacher would show the second video clip to reveal the answer. The second video clip shows the ratio of original soda in a different way that, I believe, is easier to see what really is going on. Two follow up questions that were posed by Dan Meyer were, “What if the soda didn’t mix? Would that change the answer?”

The Common Core State Standard that is addressed with this problem is 6th grade ratios and proportions.

6.RP.A.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

This activity is a great way for sixth grade students to begin to understand how ratios and proportions can play out in real-world scenarios. Although this activity is very simple it does a very good job in demonstrating how the ratio changed and how the end product was affected. By doing an activity that students can relate to and be interested in they are more likely to participate and want to figure out the answer and ultimately learn a new concept.

6.RP.3 Shower v. Bath

Shower v. Bath

The 3-acts math task, “Shower v. Bath,” by Dan Meyer can be found at http://mrmeyer.com/threeacts/showervbath/.

This activity is aligned to:

  • CCSS-Math 6.RP.3: Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

The first act is a split screen video of a guy sitting in the bath on the bottom part of the screen and him standing in the shower in the top part of the screen.  Underneath the video, there is a question: “which do you think is cheaper: a shower or bath? Why?” The second act has a video of the duration of the shower and bath. The guy takes a shower in about 2 minutes and 24 seconds and takes a bath in about 8 minutes and 10 seconds.  There is also a video of the water rate in minutes per gallon for the bath and the shower.  It takes the faucet for the bath only about 11 seconds to fill up a one-gallon jug and it takes the shower head about 27 seconds.  Then under the videos there is an image of the cost of water in Mountain View, CA.  The third act has four questions: “how would the situation have to change for the answer to reverse itself,” “how long of a shower can he have with the same amount of water he used for the bath,” “which is cheaper for you? Collect data on your own shower and bath usage,” and “which is cheaper for your class? Average the data from all your classmates.”

For the lesson, I would introduce the activity by showing my students the first act video and ask them which they think would be cheaper. A good way for the students to actively participating in the activity is to give each of the students white boards. This way they can write either bath or shower and hold up their prediction and I can choose a few students to explain why they chose their prediction.  This will get the students thinking what option would use more water and what factors go into figuring out this problem. I will have the students brainstorm what information they are going to need in order to be able to get an answer in the end. From here I will show the video of how long it takes for the man in the video to shower and bathe and how long each option takes to fill up a gallon jug. This will be a good problem for the students to really think and work through the problem.

I will formally assess the students by having each student create a small poster with comparing their data to their classmate’s data. This will have the students making graphs, charts, finding averages, and making comparisons. From the poster, it will be clear if they met the learning target.

3-Acts Math Task: Shower v. Bath

The Shower v Bath activity from Dan Myers’s Three-Acts Math tasks is about which one is cheaper, a shower or a bath. The first video shows a person taking a shower and a person taking a bath in order to set up the scenario. Then in part two it shows two videos, one showing the duration of the bath and shower, and one showing the time it takes to fill up to a gallon of water for both. Also in act two It tells you the cost of water in Mountain View, CA. In the last act the students answer questions based on the information they are provided. They have to figure out which one is cheaper, how long of a shower would they have to take to equal the same amount of water as a bath, and they will have to compare with their classmates.

http://mrmeyer.com/threeacts/showervbath/

The common core state standard for this activity is:

CCSS.MATH.CONTENT.6.RP.A.3
Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.

To achieve the common core standard I would fist show my students the fist video of the person showering and taking a bath. I would then ask my students to predict what they thought the cheaper option was and why. This will get my students thinking about the problem of which option uses more water and which option is more expensive. Next I would ask my students what information they needed to solve the problem. After discussing this and coming to an answer I will then show my students the other two videos about the duration of the shower/bath and the water rate in minutes per gallon. This will help students reason and problem solve about a real world situation using mathematics.

Question 3-6 will be a good formative assessment to see if my students have achieved the learning target. These questions will get my students thinking and using their mathematical reasoning about this real world situation. The last question asks students to compare their data with their classmates. This will get my students creating charts, diagrams, averages, and generalizing the whole real world situation. This question will help show me that my students have met the learning target.