Inca Ancient Civilization Picture Problem 4.NBT.B.4

Link amandavergara Common Core State Standards Mathematics, ML Modeling, ML Number Systems

The image displayed above could be used in an integrated math classroom to help teach 4th grade math students about mathematical practices from ancient civilizations as well as record keeping techniques. Often times, we get caught up in the paper and pencil way of showing one’s work. By integrating a bit of Inca history in our math classroom we can elicit a different form of showing work and have some creative and artistic fun while we’re at it. A rich math task to help students model adding multi-digit whole numbers is to have students learn about Inca culture and create a quipu, which is a knot technique used to add multi-digit whole numbers.

Students would be able to read about Inca life and customs and then create a quipu using numbers of their choice. Once students are taught the fundamentals about what certain knots represent and how they are positioned, they can create their own quipu that displays an algebraic equation. An extension that can be used with this task is to have students trade quipu and determine what the equation represented is and check to make sure the answer represented is correct. Another extension would be to have students divide into stations and go around to each station and use a handout to write down the equations represented on various quipu and move about the room until they have been to each quipu station.

This task is a rich math activity because it can be done by all students of varied skill levels. Advanced students  can create more complex equations, while struggling students can create much simpler equations. This task also provides multiple pathways in the sense that students can creatively represent their equations on their quipu with a variety of colors and string lengths.

The multicultural aspect of this picture activity is that it not only integrates a different form of writing math equations, but it also introduces students to Inca culture and other social studies content. Writing and literature are another integration that can be used with lesson because students read informational text about people of the Inca culture and then get an opportunity to write about how the advancements of mathematics have evolved, Inca history itself, and how students created their own quipu.

Integrated Common Core State Standards and Mathematical Practices Addressed:

CCSS.Math.Content.4.NBT.B.4
Fluently add and subtract multi-digit whole numbers using the standard algorithm.

CCSS.ELA-Literacy.RI.4.7
Interpret information presented visually, orally, or quantitatively (e.g., in charts, graphs, diagrams, time lines, animations, or interactive elements on Web pages) and explain how the information contributes to an understanding of the text in which it appears.

CCSS.ELA-Literacy.W.4.2.d
Use precise language and domain-specific vocabulary to inform about or explain the topic.

CCSS.Math.Practice.MP4 Model with mathematics.

CCSS.Math.Practice.MP5 Use appropriate tools strategically

CCSS.Math.Practice.MP6 Attend to precision.

 

 

COWculating – Picture Problem 8.F.B.4

hendrixky ML Functions, ML Modeling ,

This picture – taken from Freedom Works UK – becomes the center of a fun and highly interactive mathematics lesson where students get to think what it might be like to be a farmer! Students will be assigned a set number of cows that eat a set square footage of grass per day, and must determine how much land is needed in order to sustain the cows. Furthermore, students must consider the amount of time needed in order for grass to grow back, but they must have enough already grown for the cattle to eat in the meantime.

This lesson has students focus working on the Common Core State Standards:

CCSS.MATH.CONTENT.8.F.B.4
Construct a function to model a linear relationship between two quantities. Determine the rate of change  and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values.

CCSS.MATH.CONTENT.8.F.B.5
Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

CCSS.MATH.PRACTICE.MP2
Reason abstractly and quantitatively.

Mathematically proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abilities to bear on problems involving quantitative relationships: the ability to decontextualize—to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own, without necessarily attending to their referents—and the ability to contextualize, to pause as needed during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a coherent representation of the problem at hand; considering the units involved; attending to the meaning of quantities, not just how to compute them; and knowing and flexibly using different properties of operations and objects.

This lesson correlates to the culture of the Ellensburg area, for a large portion of this area is populated by those in the agricultural profession. While most of them are in the hay production/distribution realm, students could connect to this rural lesson nonetheless.

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

Image berrymanv Geometry Curriculum Aligned with CCSS-Math, HS Geometry, Picture Problems ,

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.

Classroom Geometry 6.G.A.1

kyleealmy Uncategorized

Math Standard:

CCSS.Math.6.G.A.1- Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.

Math Problem:

With this picture and standard I would have a worksheet for my students with a story on it. The story would include hints on things they would have to find in the classroom and solve the problem the story is asking. For example the students might have to find a right triangle in the classroom and figure out the two side lengths and then solve for the hypotenuse. I would have the students work together in teams to solve the different problems I would have set up around the room. Doing this shows the students how they use geometry in the real world. For example finding measures of the walls and solving for the area in a room. In real life you will need to know measurements of rooms when decorating, painting, building, etc. I also could have students use their tablets and the resources they have on them to solve the problems. Students can look up their own pictures and try and solve the angle measures in the pictures or they can use a tool to make shapes and solve for those shapes.

Language Arts Standard:

CCSS.LanguageArts.L.6.1- Demonstrate command of the conventions of standard English grammar and usage when writing or speaking.

Language Arts Problem:

I would incorporate this standard into this lesson because when talking in small groups and as a class I want my students to be speaking with the correct vocabulary from the lesson and use appropriate grammar. I would also have my students write a brief paragraph at the end of the lesson to see how they think they can use this in the real world. Having the students think of ways they can use it in everyday life shows the students that the lesson is not “pointless” and that “they will never use this again”.

How this lesson teaches culturally:

This lesson teaches culturally because the students will be using the tools that they learned to come together as a team or partnership to find thing around the room to solve. This is something that everyone can do at home or in the classroom. This also teaches culturally because I used student voice when I asked my students to write down how they would use this in the real world. Having students give their input and how they can use it in their life covers all areas of different cultures and lifestyles. The students are connecting it to their own life.

Playground Shapes 7.G.B.4, 7.G.B.6

cortneaaustin Common Core State Standards Mathematics ,

Problem:

For this lesson, students will be using the image of the playground to identify different two- and three-dimensional shapes they can find, and then estimating possible measurements to use to find the area, volume, and surface area of the shapes identified.

The first part of the lesson will be each student generating a list of what two- and three-dimensional objects they see. After about 5 minutes, students will have a chance to discuss and compare in groups. Once the groups have shared their findings, the class will come together to share all of the shapes and objects that are in the picture. Estimations will be determined for measurements, so that there are concrete numbers for the students to use when calculating area, volume, and surface area.

Based on the standards associated with this lesson, the main focus will be on two dimensional circles, triangles, quadrilaterals, and three-dimensional cuboid objects.

Connected math standards:

7.G.B.4 – Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship between the circumference and area of a circle.

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.

Extension:

Students who quickly progress through the shapes and objects associated with these standards can be challenged with the triangular pyramids in the picture. Also, the standard 8.G.C.9 is about using the formulas for the volumes of cones, cylinders, and spheres and using them to solve real-world problems. This is a clear extension of this activity since there are cylinders in the image, and students can be challenged to use what they know to estimate the volume of the entire slide.

Cultural relevance:

This lesson is culturally relevant to students because playgrounds are usually a place of fun for younger students, so in this way students are finding the math associated with a place that hopefully inspires positive feelings for them.

Standard from another content area:

CCSS.ELA-LITERACY.SL.7.1 – Engage effectively in a range of collaborative discussions (one-on-one, in groups, and teacher-led) with diverse partners on grade 7 topics, texts, and issues, building on others’ ideas and expressing their own clearly.

El Castillo (Temple of Kukulkan) 7.G.3

Image kristinthomas2 Uncategorized ,

Related image

Math Standard:

CCSS.Math.7.G.3 – Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.

Math Problem:

With this standard and picture, I would have students look at the different ways that this pyramid could be sliced. With each slice that they think of, I would have them draw  what the pyramid would look like from the side and top view based off of every slice they would make. This would be done in partners and  each partner group would have to come up with at least two ways that the pyramid could be sliced. As an extension, I would ask them to show what the pyramid would look like if they sliced it more than once.

Integration:

Science Standard:

MS-ESS1-1 Earth’s Place in the Universe – Develop and use a model of the Earth-sun-moon system to describe the cyclic patterns of lunar phases, eclipses of the sun and moon, and seasons.  [Clarification Statement: Examples of models can be physical, graphical, or conceptual.]

Science Problem:

After students have had the chance to look at this pyramid from different points of view as a whole piece and as slices, I would have them use the pyramid to show how the earth, sun, and moon rotate together. They would be in groups of four and have to build a physical representation of the pyramid. After they got their pyramid created, they would draw placements of the sun, moon and earth in which they would have to explain in a presentation to the class where each would be and how the placements of the earth, sun and moon would change the way the pyramid would look (e.g shadows). No one pyramid would look the same because Students would all have drawn different placement of the sun, moon and earth from the hat. After each group has presented, we then decide as a class what group’s pyramid representation would be first if we were look at it at 7:oo am and who would be next until we got to the last pyramid representation.

How this problem teaches culturally:

This problem teaches culturally because throughout this integrated unit, we would have conversations of how the pyramid was created and how the Mayans used it. We would also talk about where the pyramid is located and what the culture was like when the pyramid was built.

Taco Truck Picture Problem 4.MD.A.3

sanchezlem Picture Problems ,

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. 

World Population [Picture Problem] 8.F.B.5, L.8.3, and MP.1

kimberlyyounger Common Core State Standards Mathematics, ML Functions , , ,

By: Kimberly Younger

This image of the world, from World Mapper is skewed based off the current population in each country. Students will be assigned a country and will be asked to find out the population of the country in 1918 and the current population (2018) then they will compare the the change in population.

The lesson will focus on the standard CCSS.Math.Content.8.F.B.5 which is finding the functional relationship between two quantities, whether they are increasing or decreasing and for the this lesson they would be focusing on only linear functions. The lesson will be called Population Change Project, students will sketch the graph with the population data they collect and write a paragraph about the data the collect and interpret what it means. Including information about why they think the population increased or decreased.

This Lesson is culturally responsive because students will be learning about other countries and why the population may have increased or decreased over decade (1918 – 2018). Students could be supplied with websites which show the current population and the passed population or they can be given time to do the research on their own.

The students will use the mathematical practice of CCSS.Math.Practice.MP1 which focuses on students problem solve and preserve in solving math problems. CCSS.ELA-Literacy.L.8.3 is the use knowledge of language and its conventions when writing. The evidence of this standard would be found when students complete their write up about the change in population over the passed decade.

Creating Problems with Variables 7.EE.B.4, MP 4, W.7.2

naomijohnson2 ML Expressions & Equations, Picture Problems

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

rosasm Picture Problems , ,

 

http://blogs.ubc.ca/chefmike/files/2015/09/baked_goods.png

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.
Handout: Cookie and Brownie Recipes-1o0pzw3