Browse All

  • Filter by:

    Select Type

  • 1 - 20 of 409 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

    It’s not too hard to form the number 9 using three 3’s and any of the four standard mathematical operations +, –, × and ÷. But can you come up with four different solutions, each of which uses only one of the four operations? (Other standard mathematical symbols can be used as needed.)

    9 = 3 + 3 + 3  

    Problems
    Grades: 3rd to 5th
    Algebraic Thinking
    Write and interpret numerical expressions.
    Multiply and divide within 100.
    3.OA.C.7, 5.OA.A.1

    Assign each letter a value equal to its position in the alphabet (A = 1, B = 2, C = 3, …). Then find the product value of a word by multiplying the values together. For example, CAT has a product value of 60, because C = 3, A = 1, T = 20, and 3 × 1 × 20 = 60. 

     

    How many other words can you find with a product value of 60?

    Problems
    Grades: 3rd to 5th
    Num & Ops Base Ten
    Algebraic Thinking
    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
    The factorial of n is the product of all positive integers less than or equal to n. It is represented as n!. An example with n = 8 is shown below. With that in mind, can you find three sets of numbers (a, b, c) such that a! × b! = c! and a < b < c < 25?
    Problems
    Grades: 3rd to 5th
    Algebraic Thinking
    Multiply and divide within 100.
    3.OA.C.7
    A rectangular wooden block (not necessarily a cube) is painted on the outside and then divided into one-unit cubes. As it happens, the total number of painted faces equals the total number of unpainted faces. What were the dimensions of the block before it was painted?
    Problems
    Grades: 3rd to 5th, 6th to 8th
    Measurement & Data
    Geometry
    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

    The number groups below are the last five digits of the fifth powers of the numbers 31 through 39. However, the groups aren't in the right order to represent the fifth powers of 31 through 39 sequentially. Using only these digits, and without using a calculator, can you place the groups in the correct order?

    35393       35424       29151
    24199   21875   35168
    54432   43957   66176

     

    Problems
    Grades: 6th to 8th, 3rd to 5th
    Expression/Equation
    Num & Ops Fractions
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
    5.NF.B.5a, 6.EE.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

    Tom was born on Thanksgiving Day.

    On his seventh birthday, he noticed that Thanksgiving had never fallen on his birthday. How old will he be when he finally has a Thanksgiving birthday?

    Problems
    If x2 + y2 = 36, xy = 32, what is the positive value of x + y?
    Problems
    Grades: 9th to 12th
    Functions
    Algebra
    Interpreting Functions
    Reasoning with Equations and Inequalities
    HSA-REI.B.4b, HSF-IF.C.8a
    In the diagram at left, three different line segments each divide a quarter-circle into two regions of equal area. Rank those three segments from shortest to longest.
    Problems
    The numbers 1 through 9 are placed along the sides of the following triangle so that each side has the same sum. However, three of the nine numbers are covered. What number is in the circle with the question mark?
    Problems
    How can a cabinetmaker, using straight-line cuts, saw the two oval frames into parts that will form a circular tabletop from the parts with no waste?
    Problems
    Grades: 3rd to 5th
    Geometry
    Classify two-dimensional figures into categories based on their properties.
    5.G.B.4
    Every day in a non‑leap year, John took a different path from home to his favorite store. He walked on the grid of streets shown at left, and he only walked north or east along each street. His home is in the lower left corner of the diagram. He started on January 1, and on December 31 he took the last possible path. At what intersection is his favorite store located?
    Problems
    Make a square with 9 dots as shown. Cross all the dots with 4 straight lines without taking your pencil off the paper.
    Problems
    Grades: 3rd to 5th
    Geometry
    Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
    4.G.A.1

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

    And what is the next one after that?

    Problems
    Grades: 3rd to 5th
    Algebraic Thinking
    Gain familiarity with factors and multiples.
    4.OA.B.4
    Two chess players compete in a best-of-five match. If Chekmatova has a 60% chance of winning any particular game, what is the likelihood that she will win the match?
    Problems
    Grades: 9th to 12th, 6th to 8th
    Stats & Probability
    Conditional Probability and the Rules of Probability
    Investigate chance processes and develop, use, and evaluate probability models.
    7.SP.C.5, 7.SP.C.7a, 7.SP.C.8a, 7.SP.C.8b, HSS-CP.B.8, HSS-CP.B.9
    When the ends of the rope at left are pulled in opposite directions, how many knots will be formed along the rope's length?
    Problems
    IlluminAir is a small international airline that provides service between Toronto, Ontario; Reston, Virginia; and Doha, Qatar. There are 17 different routes from Doha to Reston, including those that go through Toronto. There are 11 different routes from Reston to Toronto, including those that go through Doha. How many routes are there from Doha to Toronto?
    Problems
    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: 3rd to 5th, 6th to 8th
    Measurement & Data
    Geometry
    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
    1 - 20 of 409 results
  • Connect with NCTM Illuminations

    Facebook icon Twitter icon YouTube icon Google+ icon Pinterest icon  

  • Most Viewed