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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
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Success Story
How many different triangles are there in the figure?
Problems
Grades: 3rd to 5th
Geometry
Classify twodimensional 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, or ?
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
x^{2} + y^{2} = 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
HSAREI.B.4b, HSFIF.C.8a
A rectangular wooden block (not necessarily a cube) is painted on the
outside and then divided into oneunit 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 realworld 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 multidigit 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
115.
Two of three arrays at left can be filled with the integers 124 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 multidigit 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 multidigit 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 multidigit arithmetic.
3.NBT.A.2, 4.NBT.B.4