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    In a four‑digit number, the sum of the digits is 10. All the digits are different. What is the largest such four‑digit number?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Num & Ops Base Ten
    Make sense of problems and persevere in solving them.
    Generalize place value understanding for multi-digit whole numbers.
    4.NBT.A.2, CCSS.Math.Practice.MP1

    Place a number in each of the following empty boxes so that the sum of the numbers in any 3 consecutive boxes is 2013. What is the number that should go in the box with the question mark?

         607                       724   ?                 
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Num & Ops Base Ten
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    3.NBT.A.2, 4.NBT.B.4, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP2

    There are 4! = 24 ways to rank four objects. However, a friend told me that if ties are allowed, the number increases to 75.

    I attempted to list all the possibilities by first listing the 24 orderings of four objects, then using brackets to group ties involving two players, then group ties involving three players, and finally the single case in which all four objects are tied. But something has gone wrong; my list includes just 69 possibilities, not 75.

    What happened? Did I miss something, or was my friend mistaken?

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

    The rectangle shown consists of eight squares. The length of each side of each square is 1 unit. The length of the shortest path from A to C using the lines shown is 6 units. 

    How many different six-unit paths are there from A to C?

    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
    The length and width of a rectangle are whole numbers of centimeters. Neither is divisible by 6. The area of the rectangle is 36 square centimeters. What is the perimeter of the rectangle, in centimeters?
    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.
    Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
    Gain familiarity with factors and multiples.
    Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
    3.MD.D.8, 4.OA.B.4, 3.MD.C.7b, 4.MD.A.3, CCSS.Math.Practice.MP1

    A calendar year is typically referred to as a four‑digit number, as in 2008, or as a two‑digit number, as in ’08. Sometimes, the two‑digit number divides evenly into the four‑digit number, with no remainder.

    How many times did this happen during the twentieth century?

    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    The Number System
    Num & Ops Base Ten
    Algebraic Thinking
    Attend to precision.
    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.
    Multiply and divide within 100.
    3.OA.C.7, 5.NBT.B.6, 6.NS.B.2, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP6

    What is the smallest positive number with exactly ten positive integer divisors?

    And what is the next one after that?

    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Algebraic Thinking
    Make sense of problems and persevere in solving them.
    Gain familiarity with factors and multiples.
    4.OA.B.4, CCSS.Math.Practice.MP1

     7772 means 777 × 777,
    7773 means 777 × 777 × 777,
    and so on.

    Suppose 7777 is completely multiplied out. What is the units digit of
    the resulting product?

    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Expression/Equation
    Num & Ops Fractions
    Algebraic Thinking
    Attend to precision.
    Make sense of problems and persevere in solving them.
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
    Multiply and divide within 100.
    3.OA.C.7, 5.NF.B.5a, 6.EE.A.1, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP6
    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
    Can you really trisect an angle with a carpenter's square?
    Problems
    Grades: High School, 9th to 12th
    Geometry
    Congruence
    HSG-CO.B, HSG-CO.C, HSG-CO.D

    How much should the manager of a theater raise his prices in order to maximize his profit?

    Problems
    Grades: High School, 9th to 12th
    Functions
    Building Functions
    Interpreting Functions
    HSF-IF.B.4, HSF-IF.B.5, HSF-IF.C.7, HSF-BF.A.1
    Find two transformations that will move one triangle onto the other.
    Problems
    Grades: High School, 9th to 12th
    Geometry
    Congruence
    HSG-CO.A.5
    A Ninja apprentice needs your help to use the density of titanium to calculate the angle of the spike on his throwing star!
    Problems
    Grades: High School, 9th to 12th
    Geometry
    Circles
    Similarity, Right Triangles, and Trigonometry
    HSG-SRT.D, HSG-C.B
    Find the dimensions of a window designed to let in the maximum amount of sunshine.
    Problems
    Grades: 9th to 12th
    Geometry
    Functions
    Modeling with Geometry
    Interpreting Functions
    HSF-IF.B.4, HSG-MG.A.3
    Which of two planes is gaining altitude more quickly?
    Problems
    Grades: High School, 9th to 12th
    Geometry
    Similarity, Right Triangles, and Trigonometry
    HSG-SRT.C.8
    Find the radius of the inscribed circle.
    Problems
    Grades: High School, 9th to 12th
    Geometry
    Circles
    Similarity, Right Triangles, and Trigonometry
    HSG-SRT.C.8, HSG-C.A.2
    A girder must be carried along a corridor that has a 90-degree turn at the end. How wide must the corridor be in order for the girder to fit around the corner?
    Problems
    Grades: 9th to 12th, High School
    Geometry
    Functions
    Similarity, Right Triangles, and Trigonometry
    Interpreting Functions
    HSF-IF.B.5, HSG-SRT.B.5
    Why can't this figure, which includes a circle and a rhombus, exist with the given measurements?
    Problems
    Grades: High School, 9th to 12th
    Geometry
    Circles
    Similarity, Right Triangles, and Trigonometry
    HSG-SRT.C.8, HSG-C.A.2
    There are 5 houses on a street: house A, B, C, D and E. The distance between any two adjacent houses is 100 feet.  There are 2 children living in house A, 3 children living in house B, 4 children living in house C, 5 children living in house D and 6 children living in house E.   If the school bus can only make one stop on that street, in front of which house should the bus stop so that the sum of walking distance among all children will be the least?
    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
    Jada has 1 penny, 2 nickels, and 1 dime. How many different sums of money can she make, if she uses at least one coin?
    Problems
    Grades: 9th to 12th, 6th to 8th, 3rd to 5th
    Mathematical Practices
    Attend to precision.
    Make sense of problems and persevere in solving them.
    CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP6
    1 - 20 of 221 results