Chelsea Cutting from Mount Gambier, South Australia, tells us about the
realworld connections her students are able to make after using
Illumination resources.
Success Story
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
Equations to solve in your
head:
Is this a joke? Not if you can
multiply the first equation by 6,751 and the second by 3,249 in your head, and
not if you use a second, simpler method.
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, HSAREI.C.6, HSAREI.C.5
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
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
Three lines cut rectangle ABCD into six congruent
(identical) squares.
The perimeter of rectangle ABCD is 30
cm. What is the area of the shaded region, in square centimeters?
Problems
Grades: 3rd to 5th
Measurement & Data
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.
3.MD.C.5a, 3.MD.C.5b, 3.MD.C.6, 3.MD.C.7a, 3.MD.C.7b, 4.MD.A.3
In bowling, the pins are numbered from 1 to 10 and
form an equilateral triangle, as shown below.
How might a bowler take
two shots in one frame such that the sum of the pins he knocked down on the
first ball equals the sum of the pins he knocked down on the second?
Note that the bowler needn’t knock down all 10 pins. Also, it must be
physically possible to knock down the pins you choose — for instance, it’s
impossible for a bowling ball to knock down pins 3, 4, and 10 without knocking
down others.
Problems
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
Algebra exercises often ask students to "Find
n
." But you won't find
n
in this brainteaser!
Create an equation of the form
c
=
ab
such that:
 When written out in English, none of the numbers
a,
b, or
c
contain the letter
n
.
 a,
b, and
c
are all integers.
 c
has the largest value possible.
Problems
Grades: 3rd to 5th
Algebraic Thinking
Multiply and divide within 100.
3.OA.C.7
Find the center of the circle using only the drafting triangle and pencil as shown.
Problems
Find four positive integers
a
,
b
,
c
, and
d
such that the product
abcd
is equal to the sum of the squares,
a^{2}
+
b^{2}
+
c^{2}
+
d^{2}
.
abcd=
a^{2}
+
b^{2}
+
c^{2}
+
d^{2}
What? That's too easy, you say? You're probably right. But can you find four different solutions 
 One that uses the same number four times?
 One that uses the same number three times?
 One that uses the same number twice?
 And, one that uses four different numbers?
Problems
Grades: 3rd to 5th
Num & Ops Base Ten
Algebraic Thinking
Use place value understanding and properties of operations to perform multidigit arithmetic.
Multiply and divide within 100.
3.OA.C.7, 3.NBT.A.2, 4.NBT.B.4
“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 multidigit arithmetic.
Multiply and divide within 100.
3.OA.C.7, 4.NBT.B.5
On the map shown, begin at Start. Travel the roads along any path you
like, following typical traffic laws, and each time you pass a number,
add it to your current sum. However, you are not allowed to pass any
number more than once. Can you reach End with a sum of 91?
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 diagram at left shows the top of a regular pentagon with the top of a square
inscribed in it. The shapes share a vertex at the top, and the other two
vertices of the square lie on the sides of the pentagon. If the diagram were
continued to include the entire pentagon and the entire square, which shape
would extend below the other?
In
other words, does the whole square fit inside the pentagon, does the square
protrude at the bottom, or do the square and pentagon meet at a single point?
Problems
Grades: 9th to 12th
Geometry
Circles
HSGC.A.3
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, HSGC.A.3
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
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
In the diagram at left, three different line segments each divide a quartercircle
into two regions of equal area. Rank those three segments from shortest to
longest.
Problems
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