Browse All

  • Filter by:

    Select Type

  • 1 - 20 of 398 results
    Jan Gebert is an Illuminations lesson plan reviewer and instructor of professional and secondary education at East Stroudsburg University. So she definitely knows a thing or two about quality lessons. Illuminations asked her for her favorite out of our 600+ lessons.
    Success Story

    Deeanna Golden, a teacher of 24 years at F.M. Golson Elementary School in Marianna, Florida, is a beloved Illuminations lesson plan writer. So we asked her, "Why do you think it is important to share resources?"

    Success Story
    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

    Water Bucket Conundrum This problem has crossed my path a number of times in various guises. Perhaps you have also seen a version of it. You are staying at a rural cabin, and the only method to get water is to draw it from a well. A 4-gallon bucket and a 9-gallon bucket are the only containers for carrying

    Problems

    Problems to Ponder: Neighborhood Sleuth

    Problems

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

    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
    Algebraic Thinking
    Measurement & Data
    Make sense of problems and persevere in solving them.
    Gain familiarity with factors and multiples.
    Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.
    Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
    Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.
    4.MD.A.3, 3.MD.C.7b, 3.MD.D.8, 4.OA.B.4, 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: 6th to 8th, 3rd to 5th, 9th to 12th
    The Number System
    Num & Ops Base Ten
    Mathematical Practices
    Algebraic Thinking
    Compute fluently with multi-digit numbers and find common factors and multiples.
    Perform operations with multi-digit whole numbers and with decimals to hundredths.
    Attend to precision.
    Make sense of problems and persevere in solving them.
    Multiply and divide within 100.
    3.OA.C.7, CCSS.Math.Practice.MP1, CCSS.Math.Practice.MP6, 5.NBT.B.6, 6.NS.B.2

    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
    Num & Ops Fractions
    Algebraic Thinking
    Expression/Equation
    Attend to precision.
    Make sense of problems and persevere in solving them.
    Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
    Multiply and divide within 100.
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    6.EE.A.1, 3.OA.C.7, 5.NF.B.5a, 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
    Algebraic Thinking
    Functions
    Num & Ops Base Ten
    Look for and make use of structure.
    Reason abstractly and quantitatively.
    Make sense of problems and persevere in solving them.
    Solve problems involving the four operations, and identify and explain patterns in arithmetic.
    Interpreting Functions
    Generalize place value understanding for multi-digit whole numbers.
    4.NBT.A.2, HSF-IF.A.3, 3.OA.D.9, 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

    Figure out how many wings are in the Biggest Bucket O' Wings.

    Problems
    Grades: 6th to 8th
    The Number System
    Compute fluently with multi-digit numbers and find common factors and multiples.
    6.NS.B
    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
    1 - 20 of 398 results