# Numeracy

Adding to 10 is but on example of a large number of spreadsheets that could be developed to practice addition. We give students two number… Continue

Multiplication is often thought of as repeated addition. By building a times table by using a repeated addition rule you will have a fun practice… Continue

Now that students can build addition tables, they should look for the patterns in them. We introduce them to a variety of things they might… Continue

From here on students can go in most any order they choose. They can start with addition or with multiplication. They should imagine themselves on… Continue

We have been using cell addresses informally until now, but now we can be more formal and explicit. Different spreadsheets have different types of address… Continue

### Associativity

Parentheses are not only important in paper math, they are critical in spreadsheets. To make sure that terms are handled properly by spreadsheets, we have… Continue

### Battleship

Spreadsheets can be a great place for you to build your own games. Ryan has built one of his early favorites, Battleship, where you learn… Continue

### Build a House

Spreadsheets with their natural grid make a great, though not entirely flexible, platform for architectural design and for working with shapes. Build a house introduces… Continue

### Build a Times Table

Students are tasked to build a times table in just two steps. They have to learn to use absolute as well as relative addressing to… Continue

### Common Denominators

We can use these proportions to compare two ratios with different denominators by finding a denominator that their proportions have in common. Thus the common… Continue

### Commutativity

The symmetry of the multiplication table around the square numbers diagonal we call commutativity or the commutative property. It means that in a 12 by… Continue

### Counting By

Counting-By introduces multiplication. Counting-by or skip-counting is, we believe, the best way to help students build their multiplication facts, and though they will live in… Continue

### Decimal Division

Decimal Division is one of a series of Labs to help you understand and learn to use decimals. I think you will find it fun… Continue

### Decimal Multiplication

Decimal Multiplication is one of a series of Labs to help you understand and learn to use decimals. I think you will find it fun… Continue

### Decimal Subtraction

Decimal subtraction is one of a series of Labs to help you understand and learn to use decimals. I think you will find it fun… Continue

### Distributivity

The distributive property turns out to be central to a surprising variety of important mathematics. One of the most valuable is to use it to… Continue

### Division and Ratio

We can make a division table just like we made a multiplication table. Division is surprisingly our most important operation in terms of most of… Continue

### Drawing Triangles

Though spreadsheets lets you put geometric shapes on the screen, those shapes are not connected with the cells and cannot be changed by using different… Continue

### Enigma Machine

Spreadsheets are great for creating secret codes and for breaking them. During World War II the German military used a machine they called Enigma to… Continue

### Factor Pairs

Multiplying creates products, factoring separates a product into the numbers that make it up. We thus start with the table and then look at the… Continue

### Factor Table

Spreadsheets always automatically perform the operations you ask them to do. But sometimes we want to see the process. We can make spreadsheets show us… Continue

### Graphing

Graphs as we know them were first invented by Galileo. They are powerful images of functions. I will introduce you to graphs by letting you… Continue

### How Many Times

How many of the numbers from 1 to 100 are in the times table? All, Most, Less than half? I think you will find in… Continue

### Hundreds Table Patterns

We introduce students to more complex patterns and rules in hundreds tables. In particular, we have students look at diagonal patterns and develop rules to… Continue

### Introducing Subtraction

What if you built a rule that would enable you to count backwards? How would it be the opposite of addition? What would happen if… Continue

### Lights Out

This is one of those math puzzles that come up in contests but which turn out to be quite interesting mathematically. Imagine a long hallway… Continue

### Magic Rectangle

Multiplication tables have some wonderful and quite surprising patterns. This is one of them. Draw any rectangle in a multiplication table and you will find… Continue

### Make a Hundreds Table

This is the graduation exercise for the basic use of spreadsheets. We combine rules and addressing to have students build their own hundreds table in… Continue

### Making Fractions

Spreadsheet math generally focuses on ratio and proportion to develop the concept of fraction. But fractions is such a big problem in today’s curriculum that… Continue

### More Number Lines

We use rules to build new numberlines. For example we can start in the middle and go both forward or backward using adding and subtracting rules. You can even… Continue

### Motion Problems

George is in New York and Martha is in Washington. They leave at the same time and follow the same road to meet each other… Continue

### Multiplying Integers

We have made a big deal of the times table and of other tables.Now we extend the times table to negative numbers and thus to… Continue

### Number Lines

Number Lines introduce students to functional thinking and the use of formulas in spreadsheets. For younger students we call these formulas “rules” and ask students… Continue

### Number Patterns

Use numberlines and spreadsheet rules to explore the amazing patterns we find in our whole numbers. Did you know that you can get the odd… Continue

### Number Series

Spreadsheets make it easy for us to explore patterns in the whole numbers. This Lab does that and helps you learn the basics of spreadsheets… Continue

### Odd Times

How many of the products in a 12 by 12 times table are odd numbers? This is a question we rarely ask in paper-based math… Continue

### Pennies to Heaven

Pennies to Heaven is a Fermi Problem, basically a “headmath” experiment. Fermi Problems, originally developed by Enrico Fermi, one of the greatest experimental and theoretical… Continue

### Place Value

Our number system inherited from India and from the Medieval Arab world enables us to use just 10 symbols to write any number we can… Continue

### Place Value: Decimals

We take our place value generator to decimals to help students see the simplicity of the place value pattern going right as well as left. Continue

### Place Value: Thousands

We extend the place value generator to 100’s of thousands to show you how the pattern of 1’s, 10’s, 100’s, continues to 1,000’s, 10,000’s, 100,000’s.… Continue

### Prime Numbers

The prime numbers are among the most fascinating objects in all of mathematics. While we can generate them, we do not know or understand their… Continue

### Products as Areas

Using the times table, students can see that products are always rectangles, and that they represent the area of that rectangle. They should explore the… Continue

### Rows and Columns

We use the hundreds table to introduce rows and columns and focus students on seeing the patterns in these tables. Again and again we go… Continue

### Shapes

Shapes introduces student to changing the colors in cells and to changing the shapes of cells by dragging the column or row separators in the… Continue

### Square Numbers

The square numbers form an interesting pattern on the times (multiplication) table. They run along a diagonal from 1 to the top right of the… Continue

### Subtraction Tables

What would a subtraction table look like? How would its pattern be different from an addition or multiplication table? Is subtraction commutative? Continue

### Sudoku Challenge

Have you ever played Sudoku? It is fun and challenging. You have to find the numbers from 1 to 9 in each cell so that… Continue

### Syracuse Problem

I built a Lab for you to play with the Syracuse Problem and to learn to use spreadsheets to play with like problems in fun… Continue

### Triangular Numbers

1, 3, 6, 10… are called the triangular numbers because they can be stacked up to form a triangle. They are very interesting numbers, and… Continue