# Mathematical Practice: MP5 - Use appropriate tools strategically.

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Mathematical Practices
Mathematical Practices
• MP1 - Make sense of problems and persevere in solving them. (82)
• MP2 - Reason abstractly and quantitatively. (47)
• MP3 - Construct viable arguments and critique others' reasoning. (56)
• MP4 - Model with mathematics. (54)
• MP5 - Use appropriate tools strategically. (39)
• MP6 - Attend to precision. (36)
• MP7 - Look for and make use of structure. (68)
• MP8 - Look for and express regularity in repeated reasoning. (61)

### Percents

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Developed as part of the Math Circles of Inquiry project, this module has students grapple with different representations of percents in various contexts in order to solve real life problems. Students need fluency in percentages for real world applications such as shopping, eating at restaurants, commission based careers, etc. Understanding percent expressions in seventh grade is necessary to be able to create exponential functions in Algebra 1.

This module contains twelve activities to address the various fine points associated with percent standards.

### Making Connections Between Forms of Quadratic Equations

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Developed as part of the Math Circles of Inquiry project, the goal of this module is to help students in Algebra II become fluent in the various forms of a parabola equation based on the information that they are given. Students sometimes fail to understand that there are multiple ways to find an equation of a parabola. This module incorporates multiple activities both in the learning packet and using Desmos activities online to encourage students to discover and practice writing equations of parabolas in their various forms. At the end of this activity students will work more efficiently with equations...

### Rational Numbers

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Developed as part of the Math Circles of Inquiry project, this module is an introductory activity for rational numbers, likely aligned with Grade 7. Students will be given five points on a number line and will be asked to estimate the values of each in a 3-part task and explain their reasoning. The activity is designed to have students then fluently add, subtract, multiply, and divide these rational numbers and justify the placement of their solutions on the number line.

### Trigonometric Ratios in Right Triangles

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Developed as part of the Math Circles of Inquiry project, this five to six day activity is designed to help students understand trigonometric ratios, by building on their understanding of similar triangles and ratios of corresponding sides. The purpose of this module is for students to spend time and energy developing the reasons the sine, cosine and tangent ratios are effective tools for solving right triangles, by analyzing patterns that emerge when the trig table is compiled from class generated data, and to understand the numbers stored in their calculator before they start using it to problem solve. An optional...

### System of Inequalities: Math Dance

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You want this year’s dance to be LIT! The dance committee has a goal of fundraising \$3,500 through ticket sales. How many tickets do they need to sell?

Developed as part of the Math Circles of Inquiry project, this module presents an engaging problem which will allow students to investigate how to graph and solve a system of inequalities.

### Magic, Latin, & Sudoku Squares

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Squares and numbers, numbers and squares. There is something very satisfying about arranging numbers in a square formation, following specific rules, whether it is a Magic Square, Latin Square or Sudoku. This is probably why Sudoku puzzles are so popular. This session touches on some of the deep mathematics behind these special squares.

### Mathemagical Card Tricks

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There are many card tricks based on simple mathematics as opposed to sleight of hand. In this session, participants will play with a number of such tricks, test them out and work on discovering the math underneath, with a goal to formalize the mathematics that makes the trick work.

### Pigeonhole Principle and Parity Problems

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The pigeonhole principle states that if n pigeons are put into m cubbies, with n > m, then at least one cubby must contain more than one pigeon. Parity problems deal with odd and even integers. Here is a collection of problems that can be used in a single problem solving session, or as individual teaser questions.

Problems are suitable for a math circle or classroom.

### Place Value Problems

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In this session, we’ll learn how to solve problems related to place value. This is one of the fundamental concepts in arithmetic, something every elementary and middle school mathematics teacher should understand profoundly. Several example puzzles are followed by a rich selection of over 30 additional problems to explore.

This collection of place value problems is suitable for student circles, teacher circles, or the classroom.

### Pick’s Theorem

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Austrian mathematician Georg Pick first stated this theorem in 1899. However it wasn’t brought to broad attention until 1969. In this exploration, participants will use rates of change to aid them in discovering Pick’s famous formula by finding a relationship between the area of the figure, the number of perimeter pegs, and the number of interior pegs.

This session is also suitable for student circles or the classroom.