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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
    How many different triangles are there in the figure?
    Problems
    Grades: 3rd to 5th
    Geometry
    Classify two-dimensional figures into categories based on their properties.
    5.G.B.4
    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

    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

    Which is bigger, \sqrt {10}  + \sqrt {29} or \sqrt {73}

    Don’t even think about using a calculator for this one.

    Problems
    Grades: 6th to 8th
    Expression/Equation
    The Number System
    Work with radicals and integer exponents.
    Know that there are numbers that are not rational, and approximate them by rational numbers.
    8.NS.A.2, 8.EE.A.2
    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
    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
    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

    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

    Ask a friend to pick a number from 1 through 1,000. After asking him ten questions that can be answered yes or no, you tell him the number.

    What kind of Questions?

     

    Problems
    Grades: 3rd to 5th
    Num & Ops Base Ten
    Generalize place value understanding for multi-digit whole numbers.
    4.NBT.A.2

     

     

    A magic rectangle is an m× n array of the positive integers from 1 to m× n such that the numbers in each row have a constant sum and the numbers in each column have a constant sum (although the row sum need not equal the column sum). Shown below is a 3 × 5 magic rectangle with the integers 1-15.

     
     
     
     
     
     
     
     
     
     
     
     
     
     
     

     Two of three arrays at left can be filled with the integers 1-24 to form a magic rectangle. Which one can't, and why not? 

    Problems

    Wheels A, B, C, and D are connected with belts as shown. If wheel A starts to rotate clockwise as the arrow indicates, can all 4 wheels rotate? If so, which way does each wheel rotate?

     

    Can all the wheels turn if all 4 belts are crossed? If 1 or 3 belts are crossed?

    Problems
    A pocket watch is placed next to a digital clock. Several times a day, the number of minutes shown by the digital clock is equal to the number of degrees between the hands of the watch. (The watch does not have a second hand.) As you can see, 10:27 is not one of those times — the angle between the hands is much greater than 27°. If fractional minutes aren’t allowed, at what times does this happen?
    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

    How do I love thee?  Let me build the ways! 

     

    Make a heart using any of the shapes in the PDF file. You can change their size, but you cannot change their shape. And you can use a shape more than once. 

     

    Can you make a heart with just three shapes? What about five? Six? Ten? How many different hearts can you make?

     

    Problems

    What is the sum of the following?

    432 + 432 + 432 + 432 + 432 + 432 + 864 + 864

    Problems
    Grades: 3rd to 5th
    Num & Ops Base Ten
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    3.NBT.A.2, 4.NBT.B.4
    The following isosceles trapezoid is composed of 7 matches. Modify the position of three matches in order to obtain two equilateral triangles.
    Problems
    Grades: 6th to 8th
    Geometry
    Draw construct, and describe geometrical figures and describe the relationships between them.
    7.G.A.2

    There are 29 students in Miss Spelling’s class. As a special holiday gift, she bought each of them chocolate letters with which they can spell their names. Unfortunately, some letters cost more than others — for instance, the letter A, which is in high demand, is rather pricey; whereas the letter Q, which almost no one wants, is relatively inexpensive.

    The price of the chocolate letters for each student in her class is shown in the table below.

    AIDEN – 386

    ARI – 209

    ARIEL – 376

    BLAIRE – 390

    CHARLES – 457

    CLARE – 334

    DEAN – 317

    EARL – 307

    FRIDA – 273

    GABRIEL – 410

    IVY – 97

    KOLE – 249

    LEIA – 317

    LEO – 242

    MAVIS – 246

    NADINE – 453

    NED – 236

    PAUL – 167

    QASIM – 238

    RACHEL – 394

    RAFI – 231

    SAM – 168

    TIRA – 299

    ULA – 148

    VERA – 276

    VIJAY – 179

    WOLKE – 272

    XAVIER – 346

    ZERACH – 355

     

    How much would it cost to buy the letters in your name?

    Problems
    Grades: High School, 6th to 8th, 3rd to 5th
    Num & Ops Base Ten
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    3.NBT.A.2, 4.NBT.B.4
    Find the center of the circle using only the drafting triangle and pencil as shown.
    Problems

    The number 4 can be expressed as the sum of three positive integers in only one way:

    4 = 1 + 1 + 2

    However, the number 50 can be expressed as the sum of three positive integers in 200 ways.

    Somewhere in between, there is a number n that can be expressed as the sum of three positive integers in precisely n ways. Can you find n?

    Problems
    Grades: 3rd to 5th
    Num & Ops Base Ten
    Use place value understanding and properties of operations to perform multi-digit arithmetic.
    3.NBT.A.2, 4.NBT.B.4
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