## Juice Containers

Using models rather than algorithms for computing with fractions.

## Camera Lens Aperture

Looking at the inversely proportional relationship between camera aperture and f-stops in photography.

## Inversely Proportional

Exploring inverse proportion within the topic of speed and time relationships.

Looking at proportion in the context of a friendly argument over sharing cookies.

## Volume and Pressure

Looking at how inverse proportion relates to science.

## Cliff or Evelyn

Address the role of place value in the algorithm for dividing decimals.

## Two Interpretations of Decimal Division

Creating story problems using two different approaches to division.

## Partial Products & Decimals

Understanding how the algorithm for multiplying decimals really works.

## Decimals as Arrays

Representing decimal products using area models.

## Let’s Help Ms. Lee

Considering multiple approaches to a decimal division problem.

## Joel’s Solution

Checking the validity of Joel’s decimal division problem.

## Two Models of Decimal Division

Explaining decimal division using various representations.

## Base-Ten Block Multiplication

Thinking about student understanding of appropriate units.

## Mixed Up?

Using mathematics to determine if two drink recipes should taste the same.

## Decimal Division

How are the three problems related?

## Bigger or Smaller?

Without calculating, determine the smaller product.

## Representing Decimals

Using Base-10 blocks to represent decimals.

## Fundraising

Comparing four fundraising group results.

## Laurel’s Muffins

Reducing a muffin recipe.

## Drink Mixes

Mixing juice while working with fractions.

## More Fraction Situations

Working with story problems.

## Increasing Population

Which city had the greatest percentage increase in population?

## Dueling Speakers

Two speakers have different ways to divide fractions. Which one is right?

## Another Folder Sale

Determining how many and at what price folders were sold.

## Pizza Party

Determining the greatest number of pizzas that the class can purchase.

## What Coins?

Using different combinations of coins.

## Money Puzzle

Solving problems using different coin valuations.

## Broken Calculator Problems

Solving problems with a broken calculator!

## Fractional Situations

Solving problems without using any kind of computational algorithm.

## What Happens When?

What happens when you multiply and divide fractions?

## Estimating the Point

Help Miriam decide if her estimation approach will work for all decimals.

## Beaker Comparison

Help Sam and Morgan decide who has more liquid in their beakers.

## Exploring Multiplication with Fractions

Exploring the similarities and differences in the steps taken to find the products.

## Exploring Division with Fractions

Exploring the similarities and differences in the steps taken to find the quotients.

## Smaller Quotient

Determining why the quotient for one problem is smaller than the quotient of another.

## 3 ÷ ½

Using visual models can help students better understand mathematics problems. Often, using visual models can help students better understand mathematics problems. How can the following drawings be interpreted as showing the quotient for 3 ÷ ½? What real-world problem might go with each of the three diagrams? a) b) c)

## Natasha’s Idea

Help decide if Natasha’s idea about dividing fractions is correct.

## Jacob’s Idea

Help decide of Jacob’s idea is correct.

## Division Pattern

Looking for patterns in division.

## The Meaning of 1/3

How can you explain the meaning of 1/3?

## How Many Servings?

Help Demetrius and BJ decide how many servings they ate.

## Decimal Diagrams

Using diagrams to show factors and products.

## Cans and Containers

How many cans does one container hold?

## Moving the Point

Why does moving the decimal point work when you multiply decimals?

## Fraction Figures

Using basic fraction operations to describe the fraction of shaded figures.

## Unit Fractions and Fibonacci

Represent unit fractions as the sum of other fractions.

## Pandigital Fraction

Examine situations with fractions that have the property of all digits from 1 to 9.

## Paper Folding

Determine the thickness of the folded paper.

## Dimes and Quarters

Determine the combination of quarters and dimes in a given amount of money.

## Counting Zeros

How many zeros are at the end of a factorial?

## Portions of 1000

Which numbers have the digit 7 as at least one of the digits?

## Log Cutting

How long does it take to cut a wooden log into a certain number of parts?

## Library Fines

Help Minerva understand her charges from the school library.

## Mailbox Letters

Find five words that are worth \$1.00.

## Fractional Triangle

Fill in the circle using fractions so that each side of the triangle will have a particular sum.

## Using Up Digits

Find a multiplication sentence using the digits 1, 2, 3, 4, 5, and 6 so that the product is closest to a certain number.

## Difficult Change

Can you guess what coins I have if I tell you what I can’t give change for?

## Canceling Jumps

Find the value in simplest terms.

## The Secret Pocket

How many of each kind of coin does Keith have in his secret pocket?

## Bouncing Ball

Determine how many times a ball hits the ground.

## Collecting Dimes

How many dimes did the driver receive in his tip?

## Spending It All

Help a shopper spend \$62.

Describe a set of natural numbers that fits a certain description.

## Shopping for Plants

Help Mr. Alvarez determine which shop has the better buy on marigolds.

## Pricing Notebooks

How much did John and his twin brothers pay for one notebook?

## Folders for Sale

Determine how much the manager of a store reduced the price of a folder.

## Approximate Digit Use

Use the digits 1, 2, 3, 4, 5, 6, 7, and 8 exactly once to make two decimal numbers whose product equals a particular number.

## Growing Tree

After four years, how many feet high was a tree that Mrs. Johnson’s class planted?

## Missing Hundreds

Determine the sum of all the digits that could replace the digit d in a given number.

## Remainders of Three

Find the remainder when a large number is divided by 3.

## Johnny’s Rule

A student has “discovered” a rule for subtracting fractions. Does his method always work?

## Digital Fractions

Use the digits 0 – 9 to make the fraction 1/3.

## Mysterious Numbers

Discover some strange properties about a mysterious number.

## Can You Tell?

Multiplying, dividing, and then comparing fractions.

## Where is that fraction?

Look for patterns when multiplying fractions.

## Making Unit Fractions

Find two fractions that add up to a unit fraction.

## Musical Chairs

Compare various fractions.

## Let’s Operate on Fractions!

Using an area model, determine what operation is being performed on these fractions.

## Fractional Parts

What fractional part of a given figure is shaded?

## Those fractions in between

Find three different fractions between 3/5 and 2/3.

## Ordering Fractions

Will a student’s “easy” method to find a fraction between two given fractions always work?

## What happens when…?

Look for patterns when you multiply numbers by a number less than one.

## Decimal Products

Are the products of repeating decimals always repeating?

Think about tenths with a calculator.

## Hot Stuff

If you are in Georgia, it should be easy to find the fraction and decimal that says, “I am hot.”

## Unit Fractions: Terminating, Repeating or Never-Ending?

Investigate patterns that emerge when unit fractions are converted into decimal form.

## Boys and Girls in the Class

Explore the properties of ratio of boys-to-girls in several classrooms.