Bridges in Mathematics

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Colored Pencils

Mai and Trace have some red, yellow, and blue pencils. 

  • There are more than 14 but less than 20 pencils.
  • There are more red pencils than yellow pencils. 
  • There are more yellow pencils than blue pencils.
  • There is an odd number of each color pencil. 

How many of each color could they have?

Hint: An odd number can be divided into 2 equal groups with 1 left over.

Six Triangles

Using 6 same-sized green triangles, how many different designs can you make?

Each design must include all 6 triangles without gaps. Each triangle must match at least 1 other triangle along a side. 

The sides of the triangles should look like this when they match: 

MLC Team: People on a Mission

In additon to the key contributors we highlight here, we are grateful to the many colleagues who support our efforts to make a difference in math education.

Dog Walker

A dog walker goes by our building every day. They walk different numbers of dogs. Sometimes other people go with them, too. If 14 feet walk by, how many dogs and people could there be? What about 22 feet?

Make 1 Whole

The Egyptians used a sum of unique unit fractions to represent other fractional values. For example, they could use ½ + ¼ to represent the value ¾. The Egyptians would not have used this representation for whole numbers, but it’s interesting to explore the different ways to make 1 whole with unique unit fractions.

How can unique unit fractions be combined to form 1 whole? 


There are 8 friends sitting at 2 lunch tables. No one is sitting alone. What are some different combinations of friends at tables? 

Partial Product Finder

Partial Product Finder allows multiplication combinations to be represented as a rectangle, or array, with dimensions that match the combination.

Breanna’s Buttons

Breanna has a button collection.

  • When she puts her buttons in 3 or 7 equal groups, there are 2 buttons left over.
  • When she puts the buttons into 2 equal groups, there is 1 button left over.

How many buttons could Breanna have?

Zebra Stripes

Maya counted an odd number of stripes on a zebra’s leg. If the zebra’s leg has an even number of black stripes, how many white stripes might it have?

The Answer Is 72

Kyle wrote a story problem about a garden. The answer is 72. What could his story problem be?

Design Your Own School Bus

If you could design your own school bus, what would it look like inside? How many rows of seats would there be? How many students would sit in each row? How many students could ride your bus at once?

Running Pattern

Kimiko ran a total of 6 miles in 4 days. Each day, she ran ½ mile more than she had run the day before.

  • How many miles did Kimiko run on the first day?
  • If Kimiko continues this pattern, how many miles will she run on the eighth day?

Make Me a Quadrilateral

The purple band is one side of a quadrilateral.

  • What types of quadrilaterals can you make?
  • How do you know what types of quadrilaterals you have made?
  • Are there any types of quadrilaterals that you can't make? How do you know?

Friendly Fly Houses

Friendly flies like to live together. They live in groups of 3 in square apartments. They enjoy having neighbors in at least 2 apartments they share walls with, but they don't want neighbors on all 4 sides. That's just too much.

Pattern Shape Pictures

Ava made pictures using three pattern shapes. Each pattern shape is worth a different number of points.  She found the total number of points for each picture.

  • How many points is each shape worth?
  • Can you make a picture worth 20 points?
  • Can you make a picture worth 10 points?

Rectangle Riddle

Find as many rectangles as you can that have a perimeter that is 4 units more than the number of square units in the area.