# Picture Problem Painted Cube 6.EE

The painted cube problem is deceptively complex, and has multiple levels of understanding applied to it. Students are shown a cube broken up into smaller sections. The cube has been painted with a particular pattern based on what faces are visible from the outside of the cube. Sections with one face exposed are painted red on that exposed side. Sections with two exposed sizes are painted pink. Sections with three exposed sides are painted green. Sections with no exposed sides are unpainted, or are clear. Student’s jobs are to count how many of each painted cube there are in a given cube, as well as to devise functions so as to quickly count out how many of a particular section there are. Their answers would be written out in table form; said tables would be given to them. Students can also be asked to find out how much surface area there is in these cubes, assuming that each section is 1 inch on each side.

CCSS.Math.Content.6.EE.A.1

Write and evaluate numerical expressions involving whole-number exponents.

CCSS.Math.Content.6.EE.A.2

Write, read, and evaluate expressions in which letters stand for numbers.

CCSS.Math.Content.6.EE.B.5

Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.

CCSS.Math.Content.6.EE.B.6

Use variables to represent numbers and write expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.

CCSS.Math.Content.8.EE.A.2

Use square root and cube root symbols to represent solutions to equations of the form x2 = p and x3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

 2x2x2 cube Green Pink Red unpainted How many? What’s the equation?

 3x3x3 cube Green Pink Red unpainted How many? 12 What’s the equation?

 4x4x4 cube Green Pink Red unpainted How many? What’s the equation?

 5x5x5 cube Green Pink Red unpainted How many? 54 What’s the equation?

 NxNxN Green Pink Red unpainted How many? 4n 6(n-2)^2 What’s the equation?

The world’s largest cookie was baked by Immaculate Baking Company in Flat Rock, North Carolina in 2003. The area of the top of this cookie was 8,120 square feet with a diameter of 101 feet and weighed 40,000 pounds. Assuming that the cookie is a perfect cylinder, and its height was 6 inches, what is its volume? Round to the nearest cubic foot.

If there was an oven that could fit this cookie inside, what is the smallest volume size that the oven could be? (Hint: the oven must be a cube).

In this lesson, students will be using their knowledge of area and volume as well as mathematical reasoning to solve a problem that involving circles, cylinders, and cubes. The picture and the problem will intrigue students because they won’t believe that a real cookie was this big until they see it for themselves. Plus, who doesn’t love cookies? The teacher could also gain incentive and interest from the students by bringing in or having the students bring in cookies after the lesson.

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.

CCSS.MATH.PRACTICE.MP1

Make sense of problems and persevere in solving them.

CCSS.MATH.PRACTICE.MP2

Reason abstractly and quantitatively.

# Gold Medal Problem 6.RP.A.3.C, MP3, MP6

Gold Medal Problem

By: Natasha Smith

BRONZE, SILVER, and GOLD… what place will you get?

As you can tell from the above picture, the U.S. takes home the gold when it comes to the Olympics. But have you ever wondered why they are able to take home so many medals?

In this lesson, students will discuss what effects how many medals a country receives at the Olympics. They will use data for the 2016 Olympics and calculate the percentage of medals each country received. Students will then compare and discuss the relationship between the percentage of medals each country received and its population and national wealth.

This lesson integrates Social Studies as students are looking at countries from all over the world and discussing how their different circumstances may affect their ability to receive Olympic medals. This lesson is culturally responsive as students will be critically thinking about how different countries may have advantages to winning Olympic medals and students may begin to realize that where you are from has a huge impact on your ability to medal. This lesson will also peak students interest as many of them follow the Olympics and idolize the athletes.

Extention: After comparing the data as a class, students will try and determine other factors that may have an impact on a country’s medal count. They will research and find their own data and decide whether or not they think the factor contributes to the amount of Olympic medals a country receives.

Math Standards:

CCSS.MATH.CONTENT.6.RP.A.3.C

CCSS.MATH.PRACTICE.MP3

CCSS.MATH.PRACTICE.MP6

Possible Social Studies Standard:

G.L.E.5.4.1: Analyzes multiple factors, compares two groups, generalizes, and connects past to present to formulate a thesis in a paper or presentation.

SaveSave

SaveSave

SaveSaveSaveSave

SaveSave

SaveSave

SaveSave

SaveSave

# Apartment Proportions 7.G.A.1

## Apartment Proportions

#### Problem:

Congratulations! You just got your first apartment. It’s located right in the heart of downtown Ellensburg. You just realized you do not have anything to put in your new living room which is 14’ by 12.5’.

Sadly, the store you want to get your furniture from only has a few options but they come in multiple proportions. Make sure you have at least one item from each of the categories. If an item is too large or small, use ratios to change the proportions. You are only allowed to have ten of the following items in your living room!

Hint: Do some of the sizes seem odd? You should probably use ratios to change the size.

Below are the furniture you can select from with the measurements.

Seating                                                            Misc

Couch 8’x4’                                                    Lamp 4’x4’

Chair 2’x3’                                                     Fan 4’x2’

Bean bag square 3’x3’                                  Bookshelf 3’x2’

Table                                                              Entertainment

Coffee Table 16’x9’                                       TV with stand 12’x10

Side Table .5’x.5’                                           TV 10’x2’

Gaming Consoles 4’x6’

Rug

Fuzzy Rug 15’x8’

Rug 14’x6’

This picture was found at Clipart-Library. This lesson will focus on the CCSS.Math.Content.7.G.A.1 which is solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and reproducing a scale drawing at a different scale.

I would teach this culturally by understanding that all students come from different cultures and different cultures have different housing expectations.

#### Other standard:

CCSS.ELA-Literacy.W.7.4
Produce clear and coherent writing in which the development, organization, and style are appropriate to task, purpose, and audience.

# Yeah He Caught It, But How Far Was It? 8.G.B.7

Problem: For this lesson, students will be doing an extreme version of utilizing the Pythagorean Theorem. The number in the picture, 400ft, is the distance from home plate to dead center field at Miller Park in Milwaukee, Wisconsin. The goal of the lesson is for students to find the distance of the ball when it is caught by Keon Broxton. Almost all of the information is present in the picture without much background knowledge, but they will also be told that he was estimated to be about 4ft off of dead center when he caught the ball.

The beginning of the lesson will have students discussing what information they have and what information they will need to complete the assignment. The groups will realize that they need to use the Pythagorean Theorem to solve the problem. The groups will come together for a class discussion and asked what information they still need.

After that, students will do their own research to find the missing components. These components are things like where in the stadium the ball was caught, where the ball was when it was caught, etc. The students will use this information to solve the problem, and present to the class how they solved the problem and how they found the missing information.

Connected Math Standards:

CCSS.MATH.CONTENT.8.G.B.7
Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

CCSS.MATH.CONTENT.8.G.B.8
Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Extension: If students are grasping the content quickly, have them estimate the angle at which the ball entered Keon Broxton’s glove. This can be done using basic trigonometry, which is referenced in the standard CCSS.MATH.HSG.SRT.D.10. While this is technically beyond their grade level, they have a lot of the background knowledge needed to solve the problem so long as they have the height of the ball at the apex of its flight.

Cultural Relevance: This lesson is culturally relevant because baseball is widely played around the world, especially in Hispanic cultures like Mexico, Puerto Rico, Costa Rica, and especially in the Dominican Republic. Plus many students idolize baseball players in a way that they will like the opportunity to do extra research with certain players in them.

Standard from Another Content Area:
WA.EALR.5.4.1
Uses sources within the body of the work to support positions in a paper or presentation.

This standard will be used when students are finding extra information for the assignment.

# Taco Truck Picture Problem 4.MD.A.3

Potential problem: After designing your own taco truck, use any method to determine the following:

1. Area of each item included in your taco truck, your taco truck, and the exterior.
2. Perimeter of each item included in your taco truck, your taco truck, and the exterior.
3. Shape of each item included in your taco truck, your taco truck, and the exterior.

This picture problem includes a variety of topics that can be covered through mathematics as well as language arts, health, social studies, and even science. Instead of focusing on the usual “boring” math problems, I’d use this taco truck long-term project to teach area and perimeter, culture, food options, and language arts (writing and reading).

The CCSS-Math that this picture problem could address include:

• 3.MD.C.7: Relate area to the operations of multiplication and addition.
• 4.MD.A.3: Apply the area and perimeter formulas for rectangles in real world and mathematical problems.

Some standards from different content area that this picture problem could address includes:

• RI.4.7: Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, timelines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.
• RI.4.9: Integrate information from two texts on the same topic in order to write or speak about the subject knowledgeably.

I would use this post to teach culturally through the different context that it provides students. Often times, students are used to the usual procedural mathematics problems; or those unrealistic word problems where someone buys 70+ watermelons. Instead, I want to provide my students with a culturally different approach. Instead of using the basic units or blocks to find area and perimeter, I would have my students work on this long-term project to develop a blueprint of what they would want their taco truck to look like; including dimensions, perimeter, and area. Through this process, students would be doing research on what a taco truck is, where they can be found, and reflect on their presence in their community in social studies or language arts. Additionally, students could research the recipes to make the perfect food item-menu for their taco truck during science or health.

# Creating Linear Problems

### By Naomi Johnson

This lesson will focus on this picture and be used to teach standard 7.EE.B.4. This standard required students to used variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems. The students will solve the equations and figure out the answer to the last problem. We will then discuss how they came to the answers. They will then be given the chance to create their own problems with a system of equations using their own pictures to represent variables in equations. They will then show them to their peers which will show the other students the different cultures and individuality of everyone in class.

This lesson could be an integrated lesson with English Language Arts because the students could then write about their equations, what each picture represents, and why they chose to make them as they did. This lesson could also incorporate the student’s different cultures because they are allowed to use whatever picture they want and it can represent themselves however they would like. The students are given the freedom to bring themselves into the problems, and this includes their individuality and cultures. They can then share these cultures with their peers when they share their problems to the class.

# Better Baking 6.NS.A.1

Everyone loves a sweet treat every once in a while, but how does that effect our bodies? This activity uses mathematics and health concepts to explore how we can make better choices about the foods we consume, and make better baking choices!

For this activity, students will choose one of the two recipes provided (chocolate chip cookies or chocolate brownies), or another recipe they find online. Students will then find healthy alternatives for the ingredients, and the class will discuss what makes these alternatives better for our bodies. They will create a new recipe using as many healthy alternatives as possible, using either the list provided or resources they know are reliable. Students will need to use their knowledge of fractions and division or multiplication to make adjustments to the recipes, in order to keep the proportions the same for each ingredient.

Extension: Students will know how much of each ingredient is being used, but they will need to do research to find out the nutritional value of each ingredient. Students will work to find out how much sugar, fat, carbohydrates, and sodium are in each variation of their recipe.

CCSS.Math.Content.6.NS.A.1: Apply and extend previous understandings of multiplication and division to divide fractions by fractions.

CCSS.Math.Practice.MP5: Use appropriate tools strategically.

CCSS.Math.Practice.MP6: Attend to precision.

H3.N1.6: Understand differences between reliable and unreliable sources of nutrition information.

# Battleship 5.G.A.1

Incorporating games into any lesson will make the learning process more engaging and hands-on. This will also be a fun activity for the students to do! The game Battleship is a great way to introduce and practice graphing points on a coordinate plane.

For this activity, students will have to understand the location of points on a coordinate plane in relation to the origin (0, 0). To understand this students will be playing on a modified version of the game board for Battleship to include all four quadrants. The game board could also be modified where the students only place their battleships in the first quadrant so it better represents real world problems. I would have developed these game boards prior to the lesson, which will be a laminated sheet of paper. Students will be placed into pairs and on their game board they will place their five battleships anywhere on the graph. Then they take turns calling out coordinate points to try and sink their opponents five battleships. For each miss they will mark those boxes on the graphs with an open circle to indicate that the shot was missed on that point. However, for each hit they will x that portion out and the opponent then receives another turn.

After the activity has completed, there will be a class discussion about how Battleship relates to graphing points on a coordinate plane. Additionally, the activity will acknowledge how the first number in the pair describes the location of the point from the origin on the x-axis and similarly for the y-axis.

Battleship can be integrated with history, geography, and science. For history, it can be related to when battleships were first invented and marketed, in 1943. Then connect the introduction of battleships to World War II and how it effected the war. Whereas for geography, the coordinate plane that is used to play the game on is similar to latitude and longitude lines on a map. This will lead to classroom discourse of how the crew needs to have a vast knowledge of the world map and where the latitude and longitude lines are in relation to other battleships. Additionally, this activity can be integrated within science by looking into buoyancy of the materials used in creating these massive ships. This game also could be used with the Periodic Table as the playing field for Battleship.

To teach culturally, as a class we can examine battleships for different countries. Then discuss the similarities and differences between them all. While looking at how the countries cultural influence plays a role in how their battleships appear and function.

CCSS.MATH.CONTENT.5.G.A.1: Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

CCSS.MATH.CONTENT.5.G.A.2: Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

CCSS.MATH.Practice.MP6: Attend to precision by understanding the location of coordinate points in relation to the origin when taking hits at their opponents battleship.

CCSS.MATH.Practice.MP7: Look for and make use of structure by recognizing the pattern of coordinate points in each quadrant. For instance, that a coordinate pair in the first quadrant will result in (positive, positive), in the second quadrant (negative, positive), third quadrant will be (negative, negative), and the fourth quadrant is (positive, negative).

# Creating a Pin on Your Cell Phone HSS.CP.B.9

Math Problem- How many different pins can you possibly create on your cell phone using the digits 0-9? How many different pins are possible using any given digit only once?

CCSS Math- HSS.CP.B.9 – (+) Use permutations and combinations to compute probabilities of compound events and solve problems.

This picture will help the students relate creating a pin number for their cell phone to mathematical content. This can be used for a mathematics activity in a statistics course to influence critical thinking and understanding mathematical concepts. By having the students recognize the total number of pins possible will introduce them to more complex ideas that involve permutations and combinations. The teacher can start off the lesson by using less digits and having the students work in groups to discuss and write out all the possible pins. This will actively engage them and stimulate their ability to critically think and solve problems. For further teaching, using a graphing calculator and the alphabet to create passwords can be used also.