Using models rather than algorithms for computing with fractions.
Looking at the inversely proportional relationship between camera aperture and f-stops in photography.
Exploring inverse proportion within the topic of speed and time relationships.
Looking at proportion in the context of a friendly argument over sharing cookies.
Looking at how inverse proportion relates to science.
Address the role of place value in the algorithm for dividing decimals.
Creating story problems using two different approaches to division.
Understanding how the algorithm for multiplying decimals really works.
Representing decimal products using area models.
Considering multiple approaches to a decimal division problem.
Checking the validity of Joel’s decimal division problem.
Explaining decimal division using various representations.
Thinking about student understanding of appropriate units.
Using mathematics to determine if two drink recipes should taste the same.
How are the three problems related?
Without calculating, determine the smaller product.
Use farm plots and crops to learn more about fractions.
Using Base-10 blocks to represent decimals.
Comparing four fundraising group results.
Reducing a muffin recipe.
Mixing juice while working with fractions.
Working with story problems.
Which city had the greatest percentage increase in population?
Two speakers have different ways to divide fractions. Which one is right?
Determining how many and at what price folders were sold.
Determining the greatest number of pizzas that the class can purchase.
Using different combinations of coins.
Solving problems using different coin valuations.
Solving problems with a broken calculator!
Solving problems without using any kind of computational algorithm.
What happens when you multiply and divide fractions?
Help Miriam decide if her estimation approach will work for all decimals.
Help Sam and Morgan decide who has more liquid in their beakers.
Exploring the similarities and differences in the steps taken to find the products.
Exploring the similarities and differences in the steps taken to find the quotients.
Determining why the quotient for one problem is smaller than the quotient of another.
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)
Help decide if Natasha’s idea about dividing fractions is correct.
Help decide of Jacob’s idea is correct.
Looking for patterns in division.
How can you explain the meaning of 1/3?
Help Demetrius and BJ decide how many servings they ate.
Using diagrams to show factors and products.
How many cans does one container hold?
Why does moving the decimal point work when you multiply decimals?
Using basic fraction operations to describe the fraction of shaded figures.
Represent unit fractions as the sum of other fractions.
Examine situations with fractions that have the property of all digits from 1 to 9.
Determine the thickness of the folded paper.
Determine the combination of quarters and dimes in a given amount of money.
How many zeros are at the end of a factorial?
Which numbers have the digit 7 as at least one of the digits?
How long does it take to cut a wooden log into a certain number of parts?
Help Minerva understand her charges from the school library.
Find five words that are worth $1.00.
Fill in the circle using fractions so that each side of the triangle will have a particular sum.
Find a multiplication sentence using the digits 1, 2, 3, 4, 5, and 6 so that the product is closest to a certain number.
Can you guess what coins I have if I tell you what I can’t give change for?
Find the value in simplest terms.
How many of each kind of coin does Keith have in his secret pocket?
Determine how many times a ball hits the ground.
How many dimes did the driver receive in his tip?
Help a shopper spend $62.
Describe a set of natural numbers that fits a certain description.
Help Mr. Alvarez determine which shop has the better buy on marigolds.
How much did John and his twin brothers pay for one notebook?
Determine how much the manager of a store reduced the price of a folder.
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.
After four years, how many feet high was a tree that Mrs. Johnson’s class planted?
Determine the sum of all the digits that could replace the digit d in a given number.
Find the remainder when a large number is divided by 3.
A student has “discovered” a rule for subtracting fractions. Does his method always work?
Use the digits 0 – 9 to make the fraction 1/3.
Discover some strange properties about a mysterious number.
Multiplying, dividing, and then comparing fractions.
Look for patterns when multiplying fractions.
Find two fractions that add up to a unit fraction.
Compare various fractions.
Using an area model, determine what operation is being performed on these fractions.
What fractional part of a given figure is shaded?
Find three different fractions between 3/5 and 2/3.
Will a student’s “easy” method to find a fraction between two given fractions always work?
Look for patterns when you multiply numbers by a number less than one.
Are the products of repeating decimals always repeating?
Think about tenths with a calculator.
If you are in Georgia, it should be easy to find the fraction and decimal that says, “I am hot.”
Investigate patterns that emerge when unit fractions are converted into decimal form.
Explore the properties of ratio of boys-to-girls in several classrooms.