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:
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, or ?
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,
,
,
,
, 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 ,
where C is the circumference, but
please do not make a mistake. The diameter of the log is not .
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