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    A bowl contains 75 candies, identical except for color. Twenty are red, 25 are green, and 30 are brown. Without looking, what is the least number of candies you must pick in order to be absolutely certain that three of them are brown?
    Problems
    Grades: 9th to 12th, 6th to 8th
    Stats & Probability
    Using Probability to Make Decisions
    Investigate chance processes and develop, use, and evaluate probability models.
    7.SP.C.5, 7.SP.C.7a, HSS-MD.B.5a
    Write 2014 with the first four prime numbers, with the aid of the operations addition, multiplication and exponentiation.
    Problems
    Grades: 6th to 8th, 3rd to 5th
    Expression/Equation
    Algebraic Thinking
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Gain familiarity with factors and multiples.
    Multiply and divide within 100.
    3.OA.C.7, 4.OA.B.4, 6.EE.A.1
    A figure resembling a spiral is shown with 35 matches. Move 4 matches to form 3 squares.
    Problems
    Grades: 6th to 8th
    Geometry
    Draw construct, and describe geometrical figures and describe the relationships between them.
    7.G.A.2
    Determine the relationships between radius, diameter, circumference and area of a circle by using a MIRA tool.
    Lesson Plan
    Grades: 6th to 8th
    Geometry
    Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
    Draw construct, and describe geometrical figures and describe the relationships between them.
    7.G.A.2, 7.G.B.4
    Model linear functions using Barbie dolls and rubber bands.
    Lesson Plan
    Grades: High School, 6th to 8th, 9th to 12th
    Stats & Probability
    Interpreting Categorical and Quantitative Data
    Investigate patterns of association in bivariate data.
    8.SP.A.1, 8.SP.A.2, 8.SP.A.3, HSS-ID.B.6a, HSS-ID.B.6c, HSS-ID.C.7

    Equations to solve in your head:

    \begin{array}{l}
 6,751x + 3,249y = 26,751 \\ 
 3,249x + 6,751y = 23,249 \\ 
 \end{array}

    Is this a joke? Not if you can multiply the first equation by 6,751 and the second by 3,249 in your head, and not if you use a second, simpler method.

    Problems
    Grades: 9th to 12th, 6th to 8th
    Algebra
    Expression/Equation
    Reasoning with Equations and Inequalities
    Analyze and solve linear equations and pairs of simultaneous linear equations.
    8.EE.C.8b, HSA-REI.C.6, HSA-REI.C.5

    How do I love thee?  Let me plot the ways! 

    A heart is drawn on a coordinate plane by plotting the following points and connecting them:

    • The coordinates of the points are:

    ( n , n ), ( n - 3, n + 3), ( n - 6, n ), ( n - 9, n + 3), ( n - 12, n ), ( n - 12, n - 3), ( n - 6, n - 9), and ( n , n -3).

    • The coordinates of one point are (2, 14).
    • All coordinates are positive integers.

    What is the value of  n ?

    Problems
    Grades: 6th to 8th, 3rd to 5th
    The Number System
    Geometry
    Apply and extend previous understandings of numbers to the system of rational numbers.
    Graph points on the coordinate plane to solve real-world and mathematical problems.
    5.G.A.1, 5.G.A.2, 6.NS.C.6b, 6.NS.C.6c, 6.NS.C.8
    Emma, a new employee at a box factory, is supposed to make cube‑shaped jewelry boxes. Help Emma determine how many different nets are possible and analyze the resulting cubes.
    Lesson Plan
    Grades: 6th to 8th
    Geometry
    Solve real-world and mathematical problems involving area, surface area, and volume.
    6.G.A.4
    Measure the length and width of a rectangle using both standard and non-standard units of measure.Then, discover that the ratio of length to width of a rectangle is constant.
    Lesson Plan
    Grades: 6th to 8th
    Ratio & Proportion
    Stats & Probability
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Investigate patterns of association in bivariate data.
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.1, 8.SP.A.1, 8.SP.A.2, 7.RP.A.2a
    Offers a method for finding the slope of a line from its graph. 
    Lesson Plan
    Grades: 6th to 8th, High School, 9th to 12th
    Ratio & Proportion
    Functions
    Expression/Equation
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Interpreting Functions
    Use functions to model relationships between quantities.
    Understand the connections between proportional relationships, lines, and linear equations.
    8.EE.B.6, 8.F.B.4, HSF-IF.B.6, 7.RP.A.2b

    Which is bigger, \sqrt {10}  + \sqrt {29} or \sqrt {73}

    Don’t even think about using a calculator for this one.

    Problems
    Grades: 6th to 8th
    Expression/Equation
    The Number System
    Work with radicals and integer exponents.
    Know that there are numbers that are not rational, and approximate them by rational numbers.
    8.NS.A.2, 8.EE.A.2

    The Fibonacci sequence is shown below, with each term equal to the sum of the previous two terms. If you take the ratios of successive terms, you get 1, 2, \frac{3}{2} , \frac{5}{3} , \frac{8}{5} , \frac{{13}}{8} , and so on. But as you proceed through the sequence, these ratios get closer and closer to a fixed number, known as the Golden Ratio.

    1, 1, 2, 3, 5, 8, 13, …  

    Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?

    Problems
    Grades: 6th to 8th, 9th to 12th
    Ratio & Proportion
    Functions
    Stats & Probability
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Interpreting Functions
    Investigate patterns of association in bivariate data.
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.1, 8.SP.A.1, HSF-IF.A.3, 7.RP.A.2a
    See first hand the sheer size of 1 million while introducing sampling and its use in mathematics.
    Lesson Plan
    Grades: 6th to 8th
    Stats & Probability
    Ratio & Proportion
    Use random sampling to draw inferences about a population.
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.3a, 7.RP.A.3, 7.SP.A.1, 7.SP.A.2
    Extend the Fibonacci Sequence through an algebra exploration.
    Lesson Plan
    Grades: 6th to 8th, 9th to 12th
    Ratio & Proportion
    Functions
    Stats & Probability
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Interpreting Functions
    Investigate patterns of association in bivariate data.
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.1, 8.SP.A.1, HSF-IF.A.3, 7.RP.A.2a
    Use a clinometer (a measuring device built from a protractor) and isosceles right triangles to find the height of a building.
    Lesson Plan
    Grades: 6th to 8th
    Stats & Probability
    Develop understanding of statistical variability.
    Summarize and describe distributions.
    6.SP.A.3, 6.SP.B.5c, 6.SP.B.5d, 6.SP.A.1

    A plywood sheet is 45 by 45 inches. What is the approximate diameter of the log the sheet was made from?

     

    The diameter d of a circle equals \frac{C}{\pi }, where C is the circumference, but please do not make a mistake. The diameter of the log is not \frac{{45}}{\pi }.

    Problems
    Grades: 9th to 12th, 6th to 8th
    Geometry
    Geometric Measurement and Dimension
    Circles
    Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
    7.G.B.4, HSG-C.A.3, HSG-GMD.A.1
    What is the smallest integer that can be the hypotenuse of two different right triangles, each of which has legs whose lengths are also integers?
    Problems
    Grades: 9th to 12th, 6th to 8th
    Geometry
    Similarity, Right Triangles, and Trigonometry
    Understand and apply the Pythagorean Theorem.
    8.G.B.7, HSG-SRT.C.8
    A brick measures 5 × 6 × 9 inches, and all faces are covered with 1‑inch square tiles. If you were to draw a straight line connecting opposite corners of each face, on which face would the diagonal line cross the most tiles?
    Problems
    Grades: 6th to 8th
    Ratio & Proportion
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.1

    In the chart, color each square according to the clues below.

    • Two positive odd numbers that have a sum of 40 and the largest possible product.
    • The smallest square number that is the sum of two non‑zero square numbers.
    • The next five numbers in the arithmetic sequence 8, 19, 30, __, __, __, __, __.
    • The maximum possible number of givens in a standard 9 × 9 Sudoku grid that does not render a unique solution.
    • Two different odd numbers, one of whose digits are the reverse of the other, whose sum is 154.
    • The two prime numbers whose product is 4 less than 5 2 .
    • In a normal distribution, the percent of values within one standard deviation of the mean.
    • The 43 rd positive even number.
    • The first four positive multiples of 4.
    • The integer lengths of three sides of a right triangle whose area is 600 square units.
    • The value of the sum 2 0 + 2 1 + 2 2 + 2 3 .
    • The value of the sum 2 0 + 2 1 + 2 2 + 2 3 + 2 4 .
    Problems
    Grades: 6th to 8th, 9th to 12th, 3rd to 5th
    Expression/Equation
    Functions
    Stats & Probability
    Num & Ops Base Ten
    Algebraic Thinking
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Interpreting Functions
    Summarize and describe distributions.
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    Generate and analyze patterns.
    Gain familiarity with factors and multiples.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    Multiply and divide within 100.
    3.OA.C.7, 3.OA.D.9, 3.NBT.A.2, 4.OA.B.4, 4.OA.C.5, 4.NBT.B.4, 4.NBT.B.5, 6.SP.B.5c, HSF-IF.A.3, 6.EE.A.1
    Use volume and unit rates to determine best values for hay bales.
    Lesson Plan
    Grades: 6th to 8th
    Geometry
    Expression/Equation
    The Number System
    Ratio & Proportion
    Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
    Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
    Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Solve real-world and mathematical problems involving area, surface area, and volume.
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.1, 6.RP.A.2, 6.RP.A.3b, 6.RP.A.3c, 6.G.A.2, 7.RP.A.1, 7.NS.A.3, 7.EE.B.3, 8.G.C.9
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