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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.

 

 

You Bakin’ Me Crazy with these Functions! 8.F.B.4, 8.F.B.5, MP.4

Link danielledowning ML Functions, ML Modeling

Students dive into the food industry when they are asked to design their own Food Trucks. A summative project based learning assessment will challenge students to analyze the importance of functions in the real-world. This is an eighth grade modeling lesson with linear function models and graphs. Students will be working in groups on their journey of creating a multi-variable function and visually represent as well as connect through a graph.

 

You Bakin’ me Crazy with these Functions Lesson-14f6nkp

Bouncing Ball – MATH.CONTENT.6.EE.C.9 & MATH.CONTENT.6.EE.A.2.C

Link nelsokar Common Core State Standards Mathematics, HS Functions, Technology Teaching Issues

downloadBasketball, soccer ball, racquetball, bouncy ball; what child does not like to play with a ball!?

So why not have a math lesson that appeals to their interest of bouncing balls!

 

 

Picture a bouncing ball. As the ball makes contact with the floor, the ball rises and slows, then descends and speeds up. For any one of those bounces, the ball’s height can be plotted as a function of time, making a parabolic shape. Therefore, the relationship between the height and time for any bounce of the ball is a quadratic.

The relationship between the graph and the bouncing ball is expressed as

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where y is representing the height of the ball at any given time x. Another form of the quadratic equation is

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where h is the x-coordinate of the vertex, k is the y-coordinate of the vertex, and a is a parameter. This form of the quadratic equation is called the vertex form.

In this activity, students will use a Motion Detector, along with a TI-Nspire, to record the motion of a bouncing ball. Once the students have collected the data, they will analyze the data and model the ball’s height as a function of time during one bounce using the standard quadratic equation, as well as the vertex form of the quadratic equation.

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This activity’s objective meets two of the Common Core State Standards:

  1. MATH.CONTENT.6.EE.C.9
    Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
  2. MATH.CONTENT.6.EE.A.2.C
    Evaluate expressions at specific values of their variables. Include expressions that arise from formulas used in real-world problems. Perform arithmetic operations, including those involving whole-number exponents, in the conventional order when there are no parentheses to specify a particular order (Order of Operations).

 

Bouncing Ball Activity

Motion Detector Tool

Crazy Constructions! HSG.MG.A.3

Link nelsokar HS Geometry, HS Modeling, Technology Teaching Issues

Today’s students are surrounded by technology, most of them their lives revolve around technology even. So what better way to connect with the students then using what they know best, technology! Especially in math, where the majority of students already dislike the subject, it is important to find ways to keep them interested and involved. The attached lesson, Crazy Constructions, does just that. This lesson has students using a program called GeoGebra to perform their geometric constructions. Students start by performing the series of constructions on paper, then they will recreate them on GeoGebra. This is great way for all students, regardless of ability, a chance to complete the assignment and get a pattern/picture as their end result. Some students struggle with using a compass and straight edge, this is where GeoGebra is helpful because it is very user friendly and it will give tips/hints on how to perform the construction. All the tool in GeoGebra are along the top with the hints/tips given as soon as a student selects the tool.

geogebratoolbar

There are even tutorials on the program if students are really struggling. The other benefit to GeoGebra is their instant feedback and results, this allows the students to know right away if they missed something based on the picture being shown on the program. This lesson meets the high school modeling with geometry Common Core State Standard: CCSS.MATH.CONTENT.HSG.MG.A.3 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

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The pictures/patterns students can create on GeoGebra by performing geometric constructions is endless. It is definitely worth giving this lesson a try. Students have enjoyed the fun, interactive way of performing constructions through this lesson; as well as getting to use a computer and technology instead of just their tools and paper.

LessonPlan-crazy-constructions-1dzu4ss

GeoGebra Free Download: http://www.geogebra.org/cms/en/download/