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National Council of Teachers of Mathematics: Classroom Resources
National Council of Teachers of Mathematics

NCTM is committed to offering standards-based resources that improve the teaching and learning of mathematics for each and every student.

Illuminations: Sliding Triangle
National Council of Teachers of Mathematics

What is the maximum area achieved during this process?

Illuminations: One Hundred Forty Five Doors
National Council of Teachers of Mathematics

What was his route?

Illuminations: Moving Matches
National Council of Teachers of Mathematics

Modify the position of three matches in order to obtain two equilateral triangles.

Illuminations: Nine Digit Fraction
National Council of Teachers of Mathematics

What is the largest possible three-digit result that can be obtained on the right side of the equation?

Illuminations: 2014
National Council of Teachers of Mathematics

Write 2014 with the first four prime numbers, with the aid of the operations addition, multiplication and exponentiation.

Illuminations: Golden Ratio
National Council of Teachers of Mathematics

Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?

Illuminations: A Spiral
National Council of Teachers of Mathematics

Move 4 matches to form 3 squares.

Illuminations: Candies
National Council of Teachers of Mathematics

Without looking, what is the least number of candies you must pick in order to be absolutely certain that three of them are brown?

Illuminations: Yes or No?
National Council of Teachers of Mathematics

What kind of Questions?

Illuminations: The Wolf, Goat, and Cabbage
National Council of Teachers of Mathematics

This problem can be found in eighth-century writings.

Illuminations: A Logical Draw
National Council of Teachers of Mathematics

All three announce white at the same time. Why?

Illuminations: Name Letters
National Council of Teachers of Mathematics

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

Illuminations: Magic Rectangles
National Council of Teachers of Mathematics

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

Illuminations: Equations to Solve in Your Head
National Council of Teachers of Mathematics

Solve these 2 equations in your head!

Illuminations: Heart Construction
National Council of Teachers of Mathematics

How many different hearts can you make?

Illuminations: Heart Plot
National Council of Teachers of Mathematics

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

Illuminations: Heart Graph
National Council of Teachers of Mathematics

Can you come up with one or more equations to graph a heart on the coordinate plane?

Illuminations: Same Hypoteneuse
National Council of Teachers of Mathematics

What is the smallest integer that can be the hypotenuse of two different right triangles, each of which has legs whose lengths are also integers?

Illuminations: Two Months
National Council of Teachers of Mathematics

Every year, there are two months that do not begin on the same day of the week as any other month. What are those two months?

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1 - 20 of 62 shown
National Council of Teachers of Mathematics: Classroom Resources
National Council of Teachers of Mathematics

NCTM is committed to offering standards-based resources that improve the teaching and learning of mathematics for each and every student.

Illuminations: Sliding Triangle
National Council of Teachers of Mathematics

What is the maximum area achieved during this process?

Illuminations: One Hundred Forty Five Doors
National Council of Teachers of Mathematics

What was his route?

Illuminations: Moving Matches
National Council of Teachers of Mathematics

Modify the position of three matches in order to obtain two equilateral triangles.

Illuminations: Nine Digit Fraction
National Council of Teachers of Mathematics

What is the largest possible three-digit result that can be obtained on the right side of the equation?

Illuminations: 2014
National Council of Teachers of Mathematics

Write 2014 with the first four prime numbers, with the aid of the operations addition, multiplication and exponentiation.

Illuminations: Golden Ratio
National Council of Teachers of Mathematics

Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?

Illuminations: A Spiral
National Council of Teachers of Mathematics

Move 4 matches to form 3 squares.

Illuminations: Candies
National Council of Teachers of Mathematics

Without looking, what is the least number of candies you must pick in order to be absolutely certain that three of them are brown?

Illuminations: Yes or No?
National Council of Teachers of Mathematics

What kind of Questions?

Illuminations: The Wolf, Goat, and Cabbage
National Council of Teachers of Mathematics

This problem can be found in eighth-century writings.

Illuminations: A Logical Draw
National Council of Teachers of Mathematics

All three announce white at the same time. Why?

Illuminations: Name Letters
National Council of Teachers of Mathematics

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

Illuminations: Magic Rectangles
National Council of Teachers of Mathematics

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

Illuminations: Equations to Solve in Your Head
National Council of Teachers of Mathematics

Solve these 2 equations in your head!

Illuminations: Heart Construction
National Council of Teachers of Mathematics

How many different hearts can you make?

Illuminations: Heart Plot
National Council of Teachers of Mathematics

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

Illuminations: Heart Graph
National Council of Teachers of Mathematics

Can you come up with one or more equations to graph a heart on the coordinate plane?

Illuminations: Same Hypoteneuse
National Council of Teachers of Mathematics

What is the smallest integer that can be the hypotenuse of two different right triangles, each of which has legs whose lengths are also integers?

Illuminations: Two Months
National Council of Teachers of Mathematics

Every year, there are two months that do not begin on the same day of the week as any other month. What are those two months?

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1 - 20 of 62 shown
National Council of Teachers of Mathematics: Classroom Resources
National Council of Teachers of Mathematics

NCTM is committed to offering standards-based resources that improve the teaching and learning of mathematics for each and every student.

Illuminations: Sliding Triangle
National Council of Teachers of Mathematics

What is the maximum area achieved during this process?

Illuminations: One Hundred Forty Five Doors
National Council of Teachers of Mathematics

What was his route?

Illuminations: Moving Matches
National Council of Teachers of Mathematics

Modify the position of three matches in order to obtain two equilateral triangles.

Illuminations: Nine Digit Fraction
National Council of Teachers of Mathematics

What is the largest possible three-digit result that can be obtained on the right side of the equation?

Illuminations: 2014
National Council of Teachers of Mathematics

Write 2014 with the first four prime numbers, with the aid of the operations addition, multiplication and exponentiation.

Illuminations: Golden Ratio
National Council of Teachers of Mathematics

Using the rule that defines the Fibonacci sequence, can you determine the value of the Golden Ratio?

Illuminations: A Spiral
National Council of Teachers of Mathematics

Move 4 matches to form 3 squares.

Illuminations: Candies
National Council of Teachers of Mathematics

Without looking, what is the least number of candies you must pick in order to be absolutely certain that three of them are brown?

Illuminations: Yes or No?
National Council of Teachers of Mathematics

What kind of Questions?

Illuminations: The Wolf, Goat, and Cabbage
National Council of Teachers of Mathematics

This problem can be found in eighth-century writings.

Illuminations: A Logical Draw
National Council of Teachers of Mathematics

All three announce white at the same time. Why?

Illuminations: Name Letters
National Council of Teachers of Mathematics

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

Illuminations: Magic Rectangles
National Council of Teachers of Mathematics

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

Illuminations: Equations to Solve in Your Head
National Council of Teachers of Mathematics

Solve these 2 equations in your head!

Illuminations: Heart Construction
National Council of Teachers of Mathematics

How many different hearts can you make?

Illuminations: Heart Plot
National Council of Teachers of Mathematics

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

Illuminations: Heart Graph
National Council of Teachers of Mathematics

Can you come up with one or more equations to graph a heart on the coordinate plane?

Illuminations: Same Hypoteneuse
National Council of Teachers of Mathematics

What is the smallest integer that can be the hypotenuse of two different right triangles, each of which has legs whose lengths are also integers?

Illuminations: Two Months
National Council of Teachers of Mathematics

Every year, there are two months that do not begin on the same day of the week as any other month. What are those two months?