Math Basics Lessons – Teacher Notes
The basic math lessons help student to grasp the concepts of addition, subtraction,
multiplication, division, and order of operations. With each lesson comes multiple sample
problems that enrich the experience to learn more about math. Each lesson also has a page
with randomly generated problems that can give students endless practice with the skill.
These lessons can be completed in any order, but most often will be taught in order from
addition, to subtraction, then to multiplication, then division, and finally order of
operations.
All of the lessons were created by high school students at Columbus School for Girls.
Addition:
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Students learn that addition is basically counting groups of things to find the total.
Students are encouraged to write an equation from a simple sentence – the basics of
a word problem.
Finally, on page 7, students can practice their skills and check their answers. All
practice problems are one digit addition. The numbers only go from 0 to 9, though
sums may be as high as 18.
Subtraction:
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Students learn that subtraction is basically counting things that are being taken out
of a group of things to find out how many are left.
Just like in the addition lesson, students are asked to write an equation from a
simple sentence.
On page 7, students can practice endlessly with randomly generated problems. All
problems are generated such that the child will never be faced with a negative
number. (The first number is always bigger than the second number.) Also, this is
single digit practice, so the numbers are always 9 or less.
Multiplication:
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Students learn some basic vocabulary – factors and product – and are taught that
anything times zero is always zero and anything times one is always itself.
Three groups of two apples are used to illustrate the problem 2 x 3.
Just like in the addition and subtraction lessons, students are asked to write a
multiplication problem from an illustration of five groups of four flowers.
In this lesson, students draw their own math problem with groups of objects, then
write the equation with numbers.
Arrays are introduced as a way of helping students count. Teachers should assist
students with this and explain that in the example, three groups of four and four
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groups of three are the same thing. They both result in twelve objects (or dots in the
array).
On page 7, students write their own multiplication equations and can use the array
to count up to the answer. If coloring the yellow dots is too much trouble, they can
simply count the dots, or even use the drawing palate to draw a rectangle around
the appropriate number of dots to make it easier to count.
A multiplication table is shown on page 8. Teachers should help students with
multiple different practice problems in order to help them learn how to use the
table.
On page 9, students may practice their skills with randomly generated problems.
Factors never get bigger than 5 x 12.
Finally, page 10 is a game to provide still more practice. Students are to solve the
problem, then click the “step” button to see if it’s correct. If it is correct, the book
moves one step closer to the bookshelf. If it is incorrect, the book doesn’t move. New
problems are acquired with the “New Problem” button. When the book reaches the
bookshelf, they are rewarded with a “You Win!” message.
Division:
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Students are given the option of whether they need to “review” division. This gives
students the option to skip right to the practice pages if that’s what they need.
After the review, students practice division problems with some support to help
them understand how to do the problems.
Page 5 is the page with the randomly generated division practice. All problems are
whole number answers, meaning there are no remainders and no decimal answers.
The final page is a game. Math problems drop from the top and fall down. Some of
them are correct, and some are incorrect. The player clicks on the correct problems.
Once they reach a score of 5, the game stops.
Order of Operations:
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Students learn that there is a specific order in which you must do math problems.
They start by putting things in order for getting ready for their day. This helps them
understand that order is important, not just with math, but in other areas of life as
well.
On the next pages, students learn that multiplication and division come before
addition and subtraction, and notice that the answer to the problem is not the same
if you do the order incorrectly.
On pages 6 and 7, students can practice with randomly generated problems.
On page 8 is more random number practice, but the problem is a more complicated
one. Teachers may need to support students in their solving these problems.