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    Some doctors use body-mass index (BMI) as a health risk indicator. According to The Old Farmer's Almanac 2000, BMI can be found using the formula: BMI = [(W×705)÷H]/H, where H is height in inches and W is weight is pounds. An index greater than 27 or less than 19 indicates an increased risk for health problems. Helix is 5 feet, 2 inches tall and weighs 110 pounds. Is his health at risk?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Expression/Equation
    Algebraic Thinking
    Make sense of problems and persevere in solving them.
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Use the four operations with whole numbers to solve problems.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    Represent and solve problems involving multiplication and division.
    3.OA.A.3, 3.OA.D.8, 4.OA.A.2, 4.OA.A.3, 6.EE.A.2c, CCSS.Math.Practice.MP1
    How fast does your heart beat? How long does it take for your heart to beat 1,000 times? If you started counting your heartbeats at midnight on Jan 1, 2000, when would you count the millionth beat? What about the billionth?
    Problems
    Grades: 3rd to 5th
    Num & Ops Base Ten
    Generalize place value understanding for multi-digit whole numbers.
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    3.NBT.A.1, 4.NBT.A.3

    In May 1999, two National League baseball players, Joe McEwing of the St.Louis Cardinals and Mike Lieberthal of the Philadelphia Phillies, each had the batting averages, as show below.

    Lieberthal: Bats- 132; Hits- 45; Batting Average- 0.341

    McEwing: Bats- 132; Hits- 45; Batting Average- 0.341

    Suppose McEwing then batted 0.800 (4 hits in 5 at bats), and Lieberthal was perfect (3 hits in 3 at bats). Which player now has the higher batting average? Are you surprised?

    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    The Number System
    Num & Ops Base Ten
    Num & Ops Fractions
    Algebraic Thinking
    Make sense of problems and persevere in solving them.
    Compute fluently with multi-digit numbers and find common factors and multiples.
    Perform operations with multi-digit whole numbers and with decimals to hundredths.
    Understand the place value system.
    Understand decimal notation for fractions, and compare decimal fractions.
    Use the four operations with whole numbers to solve problems.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    Multiply and divide within 100.
    Represent and solve problems involving multiplication and division.
    3.OA.A.3, 3.OA.C.7, 3.OA.D.8, 4.OA.A.2, 4.OA.A.3, 4.NF.C.7, 5.NBT.A.3b, 5.NBT.B.6, 6.NS.B.2, CCSS.Math.Practice.MP1
    Imagine that you bought a Beanie Baby® for $6, sold it for $7, bought it back for $8, then sold it for $9. How much profit did you make?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Measurement & Data
    Algebraic Thinking
    Make sense of problems and persevere in solving them.
    Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
    Use the four operations with whole numbers to solve problems.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    3.OA.D.8, 4.OA.A.3, 4.MD.A.2, CCSS.Math.Practice.MP1
    The Environmental Protection Agency (EPA) estimates for gas mileage on 1999 cars vary widely. Which of these cars should go the farthest on one tank of gas?
    Problems
    Grades: 6th to 8th, 9th to 12th, 3rd to 5th
    The Number System
    Ratio & Proportion
    Mathematical Practices
    Num & Ops Base Ten
    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.
    Compute fluently with multi-digit numbers and find common factors and multiples.
    Understand ratio concepts and use ratio reasoning to solve problems.
    Attend to precision.
    Make sense of problems and persevere in solving them.
    Perform operations with multi-digit whole numbers and with decimals to hundredths.
    7.NS.A.3, 5.NBT.B.7, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP6, 6.RP.A.2, 6.RP.A.3b, 6.NS.B.3, 7.RP.A.1, 7.NS.A.2a, 7.NS.A.2c
    If each side of the triangle in Figure 1 is 1 inch long, this means the triangle has a perimeter of 3 inches. Suppose you continued the pattern in the diagram until you reached Figure 5. What is the sum of the perimeters of all the white triangles in Figure 5?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Functions
    Algebraic Thinking
    Measurement & Data
    Look for and make use of structure.
    Attend to precision.
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Interpreting Functions
    Generate and analyze patterns.
    Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    3.OA.D.9, 3.MD.D.8, 4.OA.C.5, HSF-IF.A.3, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP6, CCSS.Math.Practice.MP7
    Suppose you love chocolate. The top of each cookie is covered with the same thickness of chocolate. If you wanted to choose the cookie with more chocolate, which would you pick?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Make sense of problems and persevere in solving them.
    CCSS.Math.Practice.MP1
    Mark McGwire became baseball's home run king in 1998 with 70 home runs. His 70th home run ball sold for slightly more than $3 million in 1999. Babe Ruth, an earlier home-run king, hit 60 in 1927. His home-run ball was donated to the Hall of Fame. Suppose that Ruth's ball was valued at $3000 in 1927 and, like many good investments, doubled its value every seven years. Would you rather have the value of Ruth's ball or McGwire's?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Expression/Equation
    Functions
    Num & Ops Base Ten
    Algebraic Thinking
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Interpreting Functions
    Perform operations with multi-digit whole numbers and with decimals to hundredths.
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    Use the four operations with whole numbers to solve problems.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    Multiply and divide within 100.
    Represent and solve problems involving multiplication and division.
    3.OA.A.3, 3.OA.C.7, 3.OA.D.8, 3.OA.D.9, 4.OA.A.2, 4.OA.A.3, 4.NBT.B.5, 5.NBT.B.5, HSF-IF.A.3, 6.EE.A.1, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2
    Take two sheets of 8.5 by 11 inch paper. Roll one into a short cylinder and the other into a tall cylinder. Does one hold more than the other?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Measurement & Data
    Geometry
    Make sense of problems and persevere in solving them.
    Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
    Geometric Measurement and Dimension
    Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
    Solve real-world and mathematical problems involving area, surface area, and volume.
    6.G.A.2, 8.G.C.9, HSG-GMD.A.3, 5.MD.C.4, 5.MD.C.5a, 5.MD.C.5b, CCSS.Math.Practice.MP1
    Two players each roll an ordinary six-sided die. Of the two numbers showing, the smaller is subtracted from the larger. If the difference is 0, 1, or 2, player A gets 1 points. If the difference is 3, 4, or 5, Player B gets 1 point. The game ends after 12 rounds. The player with the most points wins the game. Is the game fair?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Stats & Probability
    Mathematical Practices
    Using Probability to Make Decisions
    Look for and make use of structure.
    Attend to precision.
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Investigate chance processes and develop, use, and evaluate probability models.
    7.SP.C.7a, HSS-MD.B.6, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP6, CCSS.Math.Practice.MP7, HSS-MD.B.5a
    If all grape juice concentrates are the same strength, which recipe would you expect to have the strongest grape taste?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Ratio & Proportion
    Num & Ops Fractions
    Attend to precision.
    Make sense of problems and persevere in solving them.
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Understand ratio concepts and use ratio reasoning to solve problems.
    Extend understanding of fraction equivalence and ordering.
    Develop understanding of fractions as numbers.
    3.NF.A.3d, 4.NF.A.2, 6.RP.A.1, 6.RP.A.3a, 7.RP.A.3, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP6
    Suppose you found an old roll of 15¢ stamps. Can you use a combination of 33¢ stamps and 15¢ stamps to mail a package for exactly $1.77?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Ratio & Proportion
    Num & Ops Base Ten
    Algebraic Thinking
    Look for and make use of structure.
    Attend to precision.
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Understand ratio concepts and use ratio reasoning to solve problems.
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    Multiply and divide within 100.
    3.OA.C.7, 4.NBT.B.5, 6.RP.A.3a, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP6, CCSS.Math.Practice.MP7
    Every year, Arctic terns fly from the Arctic to the Antarctic and back, a distance of about 9000 miles each way. Suppose the birds fly at an average speed of 25 miles per hour for 12 hours a day. How many days of flying would be necessary to make the roundtrip?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    The Number System
    Num & Ops Base Ten
    Algebraic Thinking
    Make sense of problems and persevere in solving them.
    Compute fluently with multi-digit numbers and find common factors and multiples.
    Perform operations with multi-digit whole numbers and with decimals to hundredths.
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    Multiply and divide within 100.
    3.OA.C.7, 4.NBT.B.5, 5.NBT.B.5, 5.NBT.B.6, 6.NS.B.2, CCSS.Math.Practice.MP1
    Would you rather work seven days at $20 per day or be paid $2 the first day and have your salary double every day for a week?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Functions
    Num & Ops Base Ten
    Algebraic Thinking
    Look for and make use of structure.
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Interpreting Functions
    Generalize place value understanding for multi-digit whole numbers.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    3.OA.D.9, 4.NBT.A.2, HSF-IF.A.3, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP7
    Your team is down by one point. Your teammate, who makes free throws about three-fourths of the time, is at the free throw line. She gets a second shot if she makes the first one. Each free throw she makes is worth 1 point. If there is no time left, what are the chances you win the game without overtime?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Stats & Probability
    Mathematical Practices
    Using Probability to Make Decisions
    Conditional Probability and the Rules of Probability
    Make sense of problems and persevere in solving them.
    Investigate chance processes and develop, use, and evaluate probability models.
    7.SP.C.7a, 7.SP.C.8a, 7.SP.C.8b, HSS-CP.B.8, HSS-CP.B.9, CCSS.Math.Practice.MP1, HSS-CP.A.2, HSS-MD.B.5a
    Mara has 3 times as many dollars as her brother, Timmy. If Mara is given $20 by their mother, she will have 7 times as many dollars as Timmy. How many dollars does Timmy have?
    Problems
    Grades: 6th to 8th, 9th to 12th, 3rd to 5th
    Ratio & Proportion
    Mathematical Practices
    Functions
    Algebra
    Expression/Equation
    Algebraic Thinking
    Analyze proportional relationships and use them to solve real-world and mathematical problems.
    Make sense of problems and persevere in solving them.
    Linear, Quadratic, and Exponential Models
    Building Functions
    Reasoning with Equations and Inequalities
    Creating Equations
    Use functions to model relationships between quantities.
    Solve real-life and mathematical problems using numerical and algebraic expressions and equations.
    Represent and analyze quantitative relationships between dependent and independent variables.
    Reason about and solve one-variable equations and inequalities.
    Multiply and divide within 100.
    3.OA.C.7, 6.EE.B.6, 6.EE.C.9, 7.EE.B.4a, 8.F.B.4, HSA-CED.A.2, HSA-CED.A.3, HSA-REI.A.1, HSF-BF.A.1a, HSF-LE.A.2, CCSS.Math.Practice.MP1, 7.RP.A.2c
    Juliet bought 10 beads for $18. The beads she bought are red, blue or silver. Red beads are $1 each, blue beads are $2 each and silver beads are $5 each.  If she bought at least one of each, how many red beads did she buy?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Expression/Equation
    Algebra
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Analyze and solve linear equations and pairs of simultaneous linear equations.
    Reasoning with Equations and Inequalities
    Creating Equations
    8.EE.C.8b, HSA-CED.A.3, HSA-REI.C.6, 8.EE.C.8c, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2
    A rectangular wooden block (not necessarily a cube) is painted on the outside and then divided into one-unit cubes. It turns out that exactly half of the cubes have paint on them. What were the dimensions of the block before it was painted?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Measurement & Data
    Geometry
    Make sense of problems and persevere in solving them.
    Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
    Solve real-world and mathematical problems involving area, surface area, and volume.
    5.MD.C.3a, 5.MD.C.3b, 6.G.A.2, 6.G.A.4, 5.MD.C.4, 5.MD.C.5a, CCSS.Math.Practice.MP1
    In each of the following 5 boxes, there are some letter cards. Joseph takes exactly one letter card out of each box and spells the word ‘QUEST’. Which letter card did he take out from Box 4?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2

    In the Sudoku grid at left, only the numbers along the perimeter are shown.

    Suppose the grid was completed according to the standard Sudoku rules — each row, column and 3 × 3 square contains the numbers 1–9. Would the sum of all the missing numbers be divisible by 3?

    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Attend to precision.
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2, CCSS.Math.Practice.MP6
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