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    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

    A 40‑inch straightedge (without markings) is divided into four pieces. The length of each piece is an integer number of inches. These four pieces, when used in tandem, can be used to measure any integer length from 1 to 40 inches.

    What are the lengths of the pieces?

    Problems

    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

    A Friedman number is a number that can be represented with an expression that uses only the digits in the number. In addition, the expression can include +, –, ×, ÷, exponents and parentheses, but nothing else. For instance, 25 is a Friedman number because it can be represented as 52. A nice Friedman number is a Friedman number for which the digits occur in the same order in the expression as they do in the original number.
    So, 343 is a nice Friedman number, because it can be represented by an expression with the digits 3, 4, and 3 in the same order:

    343 = (3 + 4)3

    The first seven nice Friedman numbers are 127, 343, 736, 1285, 2187, 2502, 2592. Can you find an expression for each of them?

    Problems
    Grades: 6th to 8th, 3rd to 5th
    Expression/Equation
    Algebraic Thinking
    Apply and extend previous understandings of arithmetic to algebraic expressions.
    Write and interpret numerical expressions.
    Multiply and divide within 100.
    3.OA.C.7, 5.OA.A.1, 6.EE.A.1

    A 10 × 10 grid is painted with three primary colors (red, yellow, and blue) and three secondary colors (green, purple, and orange). The secondary colors are made by mixing equal parts of the appropriate primary colors — that is, red and yellow are mixed to make orange, red and blue to make purple, and yellow and blue to make green.

    The figure at left shows squares that were painted red and blue. No other squares were painted either red or blue. 

    Suppose that each small square requires a quart of paint. Altogether, 31 quarts of red paint, 40 quarts of blue paint, and 29 quarts of yellow paint were used to paint the entire 10 × 10 grid.

    Given this information, can you determine if there were more yellow or purple squares? And how many more?

    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
    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

    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
    A regular octagon is inscribed inside a square. Another square is inscribed inside the octagon. What is the ratio of the area of the smaller square to the area of the larger square?
    Problems
    Grades: 9th to 12th, 3rd to 5th, 6th to 8th
    Geometry
    Measurement & Data
    Ratio & Proportion
    Circles
    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.
    Understand ratio concepts and use ratio reasoning to solve problems.
    6.RP.A.1, 3.MD.C.7b, 4.MD.A.3, HSG-C.A.3
    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: 6th to 8th, 9th to 12th
    Expression/Equation
    Algebra
    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
    Melanie has 4 different colored crayons and 2 different boxes as shown below. How many different ways can Melanie put all 4 crayons into the 2 boxes so that each box has at least 1 crayon?
    Problems

    Starting at 12:00 midnight, you wait a number of minutes that is a perfect square and then look at a digital clock. The number you see (with the colon removed) is also a perfect square.

    What is the first time after midnight that this happens?

    Problems
    Grades: 3rd to 5th
    Measurement & Data
    Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.
    3.MD.A.1
    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

    “Mom, look at that license plate,” Will said.

    “What about it?” his mother asked. It didn’t seem unusual to her. The plate consisted of two sets of three digits, with the state logo between the sets.

    Will said, “All six digits are different. And when you multiply the first three digits, you get the same product as when you multiply the last three digits.”

    “So you do,” his mother said. “How many plates like that do you suppose there are?”

    “Well, that’s the cool part,” Will replied. “The number of plates like that is equal to the product of the first three digits.”

    What license plate might Will have seen?

    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

    In this multiplication example, P, E, and T represent different digits. What is the value of the three-digit number PET

      P E T

    ×      3

      T T T  

    Problems
    Grades: 3rd to 5th
    Num & Ops Fractions
    Algebraic Thinking
    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

    Ten is a triangular number, because 10 objects can be neatly arranged in an equilateral triangle.

    In general, a triangular number is a number that can be represented as a triangle with one object in the first row and each subsequent row contains one more element than the previous row. (From the picture above, you might notice that 1, 3, and 6 are also triangular numbers.)

    Order the digits 1 through 9 so that the sum of any two adjacent numbers is a triangular number.

    Problems
    Sam the Squirrel found a basket of pine cones one morning. He decided that every day he would double the number of pine cones in the basket in the morning and eat 2 pine cones out of the basket in the afternoon. At the end of the 3rd day, there were 34 pine cones in the basket. How many pine cones were in the basket when Sam the Squirrel found it?
    Problems
    Grades: 3rd to 5th
    Algebraic Thinking
    Generate and analyze patterns.
    Multiply and divide within 100.
    3.OA.C.7, 4.OA.C.5
    If you rearrange the letters S, T, O, and P, what is the probability that you’ll end up with a common English word?
    Problems
    Grades: 6th to 8th
    Stats & Probability
    Investigate chance processes and develop, use, and evaluate probability models.
    7.SP.C.5, 7.SP.C.7a
    How many different color patterns can be created by placing the circles onto the 4 × 4 grid such that each circle is placed on a square with the same number?
    Problems
    If 18 students occupy  \frac{3}{5} of the seats in the classroom, how many students would occupy  \frac{2}{3} of the seats in the room?
    Problems
    Grades: 3rd to 5th, 6th to 8th
    Num & Ops Fractions
    Ratio & Proportion
    Apply and extend previous understandings of multiplication and division to multiply and divide fractions.
    Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
    Understand ratio concepts and use ratio reasoning to solve problems.
    5.NF.B.4a, 6.RP.A.1, 6.RP.A.3a, 4.NF.B.4b, 4.NF.B.4c, 5.NF.B.7a, 5.NF.B.7b, 5.NF.B.7c
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