Solving systems of equations sometimes called simultaneous equations with graphs is simply a matter of finding out where they intersect. One of the most valuable things students can learn is to be able to visualize linear equations and systems of equations so that they can tell the quadrant where the intersection and therefore the solution …
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 this exploration of the relationship between the multiplication table products and the whole numbers as fascinating as I have. It is one of my favorite Labs because it gives us …
The usual way to make string diagrams using rubber bands or yarn on a board with nails does not allow much exploration. Mary Boole meant them as exercises in visualization. Building these diagrams using spreadsheets not only shows their versatility and capability for artistic expression, it helps students get used to using ordered pairs and …
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 to build a variety of number lines using rules. For example they can build a whole number line by creating a rule that adds 1 to the number in the …
Our good friend Larry Myatt, one of the great thinkers and leaders on the future of education, recently sent out a New Years greeting that featured What if Math. We are partnering with Larry on a number of exciting projects in 2020 that we will keep you informed of. Meanwhile, I want to introduce you …
“Could Napoleon build a 3 meter high by 1/2 meter thick wall around France with the stone from the Great Pyramid of Giza?” During the Napoleonic campaign in Egypt in 1798, a famous battle was fought outside Cairo in Embaba, in view of the pyramids, and is known as the Battle of the Pyramids…. It …
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 an elevator able to go up or down anytime they want, to find interesting floors to explore. NOTE: The addition table, like the other tables, goes up and to the …
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 axes to find the factor pairs that make the product. Once again we focus on the patterns in the times table so that you can not only go from factors …
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 that in several ways. Here we show the factors and have students build a times table showing the factors by using a special formula called Concatenate which means join together. …
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 address axes. Students can use spreadsheets as drawing tools and can create some wonderful pictures with them. Spreadsheets can thus be tools for visualizing mathematics as well as adding the …
