## What If: Summer Challenge

This May, we will be introducing our What If: Lab of the Week, bringing you topical spreadsheet labs that will keep your student engaged in spreadsheet math this summer!

## Our Courses

Our new What if Math courses now enable you to provide __courses of study__ with a unique spreadsheet interface. They include a cover “sheet” for you to personalize your portfolio and a syllabus “sheet” with links to the Labs. You can now organize, plan, and track your work; load spreadsheet Labs directly from the syllabus and add your completed Labs to turn this into your portfolio file. You can even create your own courses. We hope you like it.

## Our White Paper

It has been called the most important concept in mathematics. It birthed the scientific revolution. It enabled computer programming. In the latest incarnation, spreadsheets, it revolutionized business. Yet few of us can name it; still fewer of us can define it; and it is unlikely even a handful of us know its evolution. This idea that changed the world will now enable every child to learn mathematics as a creative experience.

## What if…

### “Wonder is the beginning of wisdom.” *Socrates*

### New Labs

- There are a wide variety of financial literacy problems. This is the kind of problem that appears on many tests.…Read more
- The rule of 72 is an old banker’s rule of thumb to find out how long it will take to…Read more
- Manage a business. The Lemonade Stand has been a business simulation developed in many different versions. We believe this is the…Read more
- Spreadsheets can be a great place for you to build your own games. Ryan has built one of his early…Read more
- Are you a coffee drinker? Small daily expenses like coffee can quickly add up. By using spreadsheets to organize cost,…Read more
- How much are your credit cards costing you? If you are like most of us, they are very expensive because…Read more
- If you commute to work or school, you understand how expensive driving can be. Choose a car in this interactive…Read more
- Which form of interest, simple or compound, is the fairest? If you were buying a house or a car which…Read more
- How should you figure out your profit? If you have an item that you are selling, should you price it…Read more
- How much money do you spend? How much money can you save? We all need to know these things, but…Read more
- Use spreadsheets to compare popular phone carriers and the plans they offer.Read more
- You just won the Lottery worth $600,000,000. You have a choice between taking it as a lump sum of $376.9…Read more
- Have you ever played Sudoku? It is fun and challenging. You have to find the numbers from 1 to 9…Read more

### Introduction to Spreadsheets

- Number Lines introduce students to functional thinking and the use of formulas in spreadsheets. For younger students we call these…Read more
- We have been using cell addresses informally until now, but now we can be more formal and explicit. Different spreadsheets…Read more
- We use the hundreds table to introduce rows and columns and focus students on seeing the patterns in these tables.…Read more
- In introducing Spreadsheets we want you to learn to build a numberline by using a…Read more
- Multiplication is often thought of as repeated addition. By building a times table by using a repeated addition rule you…Read more
- Use numberlines and spreadsheet rules to explore the amazing patterns we find in our whole numbers. Did you know that…Read more
- Spreadsheets make it easy for us to explore patterns in the whole numbers. This Lab does that and helps you…Read more

### Arithmetic

- Number Lines introduce students to functional thinking and the use of formulas in spreadsheets. For younger students we call these…Read more
- Adding to 10 is but on example of a large number of spreadsheets that could be developed to practice addition.…Read more
- Now that students can build addition tables, they should look for the patterns in them. We introduce them to a…Read more
- From here on students can go in most any order they choose. They can start with addition or with multiplication.…Read more
- We have been using cell addresses informally until now, but now we can be more formal and explicit. Different spreadsheets…Read more
- Parentheses are not only important in math, they are critical in spreadsheets. To make sure that terms are handled properly…Read more
- Spreadsheets with their natural grid make a great, though not entirely flexible, platform for architectural design and for working with…Read more
- Students are tasked to build a times table in just two steps. They have to learn to use absolute as…Read more
- The symmetry of the multiplication table around the square numbers diagonal we call commutativity or the commutative property. It means…Read more
- Counting-By introduces multiplication. Counting-by or skip-counting is, we believe, the best way to help students build their multiplication facts, and…Read more
- The distributive property turns out to be central to a surprising variety of important mathematics. One of the most valuable…Read more
- Multiplying creates products, factoring separates a product into the numbers that make it up. We thus start with the table…Read more
- Spreadsheets always automatically perform the operations you ask them to do. But sometimes we want to see the process. We…Read more
- We introduce students to more complex patterns and rules in hundreds tables. In particular, we have students look at diagonal…Read more
- This is one of those math puzzles that come up in contests here and there but which turns out to…Read more
- This is the graduation exercise for the basic use of spreadsheets. We combine rules and addressing to have students build…Read more
- We use rules to build new numberlines. For example we can start in the middle and go both forward or backward using adding…Read more
- How many of the products in a 12 by 12 times table are odd numbers? This is a question we…Read more
- Our number system inherited from India and from the Medieval Arab world enables us to use just 10 symbols to…Read more
- Using the times table students can see that products are always rectangles and that they represent the area of that…Read more
- We use the hundreds table to introduce rows and columns and focus students on seeing the patterns in these tables.…Read more
- Shapes introduces student to changing the colors in cells and to changing the shapes of cells by dragging the column…Read more
- Multiplication tables have some wonderful and quite surprising patterns. This is one of them. Draw any rectangle in a multiplication…Read more
- The square numbers form an interesting pattern on the times (multiplication) table. They run along a diagonal from 1 to…Read more
- We can make a division table just like we made a multiplication table. Spreadsheets will usually turn such tables into…Read more
- We think about ratio tables in terms of motion. Move up 2 and over 1, or move up 1 and…Read more
- We can use these proportions to compare two ratios with different denominators by finding a denominator that their proportions have…Read more
- Ratios can be written in a wide variety of different way: as fractions, as decimals, and as percents.,with a colon,…Read more
- Pennies to Heaven is a Fermi Problem, basically a “headmath” experiment. Fermi Problems, originally developed by Enrico Fermi, one of…Read more
- Fibonacci, the nickname given the great medieval mathematician Leonardo of Pisa is connected in most of our minds with the…Read more
- Another famous pattern, Pascal’s triangle, is easy to construct and explore on spreadsheets. Create a formula for any cell that…Read more
- Spreadsheets offer us a nearly unlimited ability to develop and learn from case studies using real world data. We will…Read more
- We look at world population over the past 60+ years and ask whether the earth’s population is growing faster or…Read more
- We take that great old problem of the inventor of chess and the ruler of India and use it to…Read more
- We take our place value generator to decimals to help students see the simplicity of the place value pattern going…Read more
- We extend the place value generator to 100’s of thousands to show you how the pattern of 1’s, 10’s, 100’s,…Read more
- There are a wide variety of financial literacy problems. This is the kind of problem that appears on many tests.…Read more
- The rule of 72 is an old banker’s rule of thumb to find out how long it will take to…Read more
- Picturing exponential growth, powers of 10, can be hard for any of us to imagine. The spreadsheet has the flexibility to…Read more
- We have made a big deal of the times table and of other tables.Now we extend the times table to…Read more
- Spreadsheet math generally focuses on ratio and proportion to develop the concept of fraction. But fractions is such a big…Read more
- Manage a business. The Lemonade Stand has been a business simulation developed in many different versions. We believe this is the…Read more
- 1, 3, 6, 10... are called the triangular numbers because they can be stacked up to form a triangle. They…Read more
- In introducing Spreadsheets we want you to learn to build a numberline by using a…Read more
- Multiplication is often thought of as repeated addition. By building a times table by using a repeated addition rule you…Read more
- How much are your credit cards costing you? If you are like most of us, they are very expensive because…Read more
- Decimal addition is one of a series of Labs to help you understand and learn to use decimals. I think…Read more
- Decimal Division is one of a series of Labs to help you understand and learn to use decimals. I think…Read more
- Decimal Multiplication is one of a series of Labs to help you understand and learn to use decimals. I think…Read more
- Decimal subtraction is one of a series of Labs to help you understand and learn to use decimals. I think…Read more

### Algebra

- The distributive property turns out to be central to a surprising variety of important mathematics. One of the most valuable…Read more
- This is one of those math puzzles that come up in contests here and there but which turns out to…Read more
- Parentheses are very important in spreadsheets because like all programming, spreadsheet formulas have to be very specific. A big formula,…Read more
- Fibonacci, the nickname given the great medieval mathematician Leonardo of Pisa is connected in most of our minds with the…Read more
- Another famous pattern, Pascal’s triangle, is easy to construct and explore on spreadsheets. Create a formula for any cell that…Read more
- Most museums with math exhibits have a Pascal’s triangle made up of pegs with…Read more
- Spreadsheets offer us a nearly unlimited ability to develop and learn from case studies using real world data. We will…Read more
- We look at world population over the past 60+ years and ask whether the earth’s population is growing faster or…Read more
- Linear functions are the most important functions. They pervade our everyday lives and our work. Their graph is a line…Read more
- Typical algebra courses start with equations and solving equations and then move to graphing and functions. We start with functions…Read more
- We ask about the coefficients and how changing each one changes the graph of the parabola. Thus what does a…Read more
- Polynomials as a class of functions have some fascinating patterns. For example their shape changes dramatically based on whether their…Read more
- Polynomial functions are not limited to the highest term and while that term is most important in determining the shape…Read more
- Spreadsheets are not limited to algebraic functions, they can also display trigonometric functions. We are modeling the sine function, but…Read more
- We take that great old problem of the inventor of chess and the ruler of India and use it to…Read more
- The rule of 72 is an old banker’s rule of thumb to find out how long it will take to…Read more
- Spreadsheets make it very easy to switch axes and add graphs. They enable students to play with what may have…Read more
- One of the most powerful aspects of the mathematics of functions is our ability to treat them as abstract quantities…Read more
- Solving systems of equations sometimes called simultaneous equations with graphs is simply a matter of finding out where they intersect.…Read more
- Picturing exponential growth, powers of 10, can be hard for any of us to imagine. The spreadsheet has the flexibility to…Read more
- Manage a business. The Lemonade Stand has been a business simulation developed in many different versions. We believe this is the…Read more
- 1, 3, 6, 10... are called the triangular numbers because they can be stacked up to form a triangle. They…Read more
- How much are your credit cards costing you? If you are like most of us, they are very expensive because…Read more
- Spreadsheets are great for creating secret codes and for breaking them. During World War II the German military used a…Read more
- In 1941 Joe DiMaggio got a hit in 56 straight games. This record has never been beaten. Some say it…Read more
- Create, manipulate, and explore triangles in this live interactive spreadsheet. On the surface, a triangle is being drawn on a…Read more
- Which form of interest, simple or compound, is the fairest? If you were buying a house or a car which…Read more
- It was one of the most amazing visions of the future ever made. In 1965 Gordon Moore, one of the…Read more
- The prime numbers are among the most fascinating objects in all of mathematics. While we can generate them, we do…Read more
- I built a Lab for you to play with the Syracuse Problem and to learn to use…Read more
- This problem is typical of the earliest algebra problems that likely came out of India. It is interesting historically, and…Read more
- Pick a whole number, any whole number. If it is even divide it by 2, if it is odd multiply…Read more
- Let's do a little target practice with this spreadsheet projectile simulator, which will map out the flight path of an…Read more

### Geometry

- Spreadsheets with their natural grid make a great, though not entirely flexible, platform for architectural design and for working with…Read more
- Using the times table students can see that products are always rectangles and that they represent the area of that…Read more
- Shapes introduces student to changing the colors in cells and to changing the shapes of cells by dragging the column…Read more
- Parentheses are very important in spreadsheets because like all programming, spreadsheet formulas have to be very specific. A big formula,…Read more
- Fractals are a new 21st century mathematics. They are patterns that repeat themselves at various scales. This one is based…Read more
- Scatterplot graphs enable us to build shapes using spreadsheets and to practice transformational geometry. They are surprisingly flexible tools. And…Read more
- The usual way to make string diagrams using rubber bands or yarn on a board with nails does not allow…Read more
- Strings need not begin and end on axes that are at right angles to each other which we call Cartesian.…Read more
- Create, manipulate, and explore triangles in this live interactive spreadsheet. On the surface, a triangle is being drawn on a…Read more

### Probability / Statistics

- Another famous pattern, Pascal’s triangle, is easy to construct and explore on spreadsheets. Create a formula for any cell that…Read more
- Most museums with math exhibits have a Pascal’s triangle made up of pegs with…Read more
- That probability is multiplicative is not an easy concept for many of us. Using the spreadsheet with our ability to…Read more
- In 1941 Joe DiMaggio got a hit in 56 straight games. This record has never been beaten. Some say it…Read more

### Financial Reasoning

- Are you a coffee drinker? Small daily expenses like coffee can quickly add up. By using spreadsheets to organize cost,…Read more
- How much money do you spend? How much money can you save? We all need to know these things, but…Read more
- You just won the Lottery worth $600,000,000. You have a choice between taking it as a lump sum of $376.9…Read more
- Use spreadsheets to compare popular phone carriers and the plans they offer.Read more
- Which form of interest, simple or compound, is the fairest? If you were buying a house or a car which…Read more
- How should you figure out your profit? If you have an item that you are selling, should you price it…Read more
- If you commute to work or school, you understand how expensive driving can be. Choose a car in this interactive…Read more
- The rule of 72 is an old banker’s rule of thumb to find out how long it will take to…Read more

### Math and Design

- This is one of those math puzzles that come up in contests here and there but which turns out to…Read more
- Multiplication tables have some wonderful and quite surprising patterns. This is one of them. Draw any rectangle in a multiplication…Read more
- Pennies to Heaven is a Fermi Problem, basically a “headmath” experiment. Fermi Problems, originally developed by Enrico Fermi, one of…Read more
- Fibonacci, the nickname given the great medieval mathematician Leonardo of Pisa is connected in most of our minds with the…Read more
- Fractals are a new 21st century mathematics. They are patterns that repeat themselves at various scales. This one is based…Read more
- We take that great old problem of the inventor of chess and the ruler of India and use it to…Read more
- Scatterplot graphs enable us to build shapes using spreadsheets and to practice transformational geometry. They are surprisingly flexible tools. And…Read more
- The usual way to make string diagrams using rubber bands or yarn on a board with nails does not allow…Read more
- Strings need not begin and end on axes that are at right angles to each other which we call Cartesian.…Read more
- Spreadsheets can be a great place for you to build your own games. Ryan has built one of his early…Read more
- Spreadsheets are great for creating secret codes and for breaking them. During World War II the German military used a…Read more
- It was one of the most amazing visions of the future ever made. In 1965 Gordon Moore, one of the…Read more
- Have you ever played Sudoku? It is fun and challenging. You have to find the numbers from 1 to 9…Read more
- I built a Lab for you to play with the Syracuse Problem and to learn to use…Read more
- How many of the numbers from 1 to 100 are in the times table? All, Most, Less than half? I…Read more
- Let's do a little target practice with this spreadsheet projectile simulator, which will map out the flight path of an…Read more