Tag: multiplication

August 30, 2012

August 29th, 2012

Dear Multipliers,

Knowing your multiplication and division facts is the key to 5th grade. It makes everything easier. Adding and subtracting fractions is a piece of cake. Finding area and perimeter is a walk in the park. Doing long division is as easy as winter shaking leaves from the trees.

Sure, you could try to memorize your multiplication facts with flash cards. But I think it’s better to internalize them by playing games, drawing pictures, and doing activities that really help you understand what multiplication is. Making arrays and describing them with number models is one good exercise.

Today, we’ll talk about factors, which are the numbers we multiply to make a product. When we find a product’s factors, it’s like looking at that number’s fingerprint–factors are what make each number unique.

Sincerely,

Mr. Heimbuck
August 29, 2012

August 28th, 2012

Dear Array Makers,

I like to think of math as the process of making models. Models help us better understand things because models break those things into their parts. We don’t just make models of trains, cars, and airplanes, however; we can also make models of numbers.

One way we can make a model of a multiplication problem is with an array. You have been working with arrays since Second Grade, and you see them all the time in everyday life. For homework this week, you will collect and bring to class arrays that you notice in the real world. One of the main jobs of a mathematician is to see math coursing through everyday life. Rather than just seeing a muffin tin as a muffin tin, a mathematician sees it as a 3×4 rectangular array.

If you have a firm grasp of arrays, you will be prepared for much of what we’ll learn in 5th grade–multiplication, fractions, percents, and area, just to name a few.

Let’s have a great day,

Mr. H
4 October 2011

October 4th, 2011

Dear Calculators,

Before we had electronic calculators and computers, human beings created ingenious methods for calculating large numbers. Only recently have electronic calculators become cheap enough that anyone can have one. Before that, humans used mechanical calculators or simple devices to help them calculate. The abacus is one example that you’ve all seen. Today, we’ll create another calculating device called Napier’s Bones. You will notice that Napier’s Bones look a lot like the lattice method of multiplication. That’s because Napier borrowed that algorithm from people in the Middle East who had been using it for hundreds of years.

If you’re patient in the construction and use of Napier’s Bones, they will not only help you calculate multiplication problems, but they will also help you better understand what exactly multiplication is and what it does.

Sincerely,

Mr. H
3 October 2011

October 3rd, 2011

Dear Rectangle Makers,

This week we’ll learn a few different algorithms for multiplication. While these step-by-step processes might look a lot different, they’re really all just the same. When we multiply, we’re making rectangles. One factor is the base. The other factor is the height. The product is the area. The different algorithms are just different methods for counting up the pieces of that rectangle.

The algorithms we’ll learn are the methods that people throughout history have devised to solve problems. We learn all of the algorithms because there’s never only one right way to solve a problem. Also, it’s a lot of fun to play with numbers.

Sincerely,

Mr. H
30 September 2011

September 30th, 2011

Dear Estimators,

Math is like horseshoes–most of the time, close enough is good enough. Usually, an estimate will give us the information we need. Sometimes, however, we have to be precise. Good mathematicians have to know how to do both. More importantly, good mathematicians have to know when estimates are appropriate and when it’s time to calculate precisely. As always, math thinking is about creating a method for solving a problem, not just doing the arithmetic.

Today, we’ll make magnitude estimates for products. The orders of magnitude are the powers of ten–1, 10, 100, 1000, 10,000, etc. By estimating the magnitude of the product, we’ll not only be able to check our calculations, but we’ll learn about the wonders of our number system. That’s really what it’s all about.

Sincerely,

Mr. H

Tag: multiplication

August 30, 2012

August 29, 2012

4 October 2011

3 October 2011

30 September 2011