Week 1: Foundations: fractions, angles, and perimeter

Field Book

1 to 4

Due

No test this week

Method

Paper first, every step

Everything this year is built with the tools in this first week. Fractions that behave, angles you can name on sight, and the habit of measuring all the way around a figure. None of it is new; all of it has to be automatic.

What you have to be able to do

Add, subtract, multiply, and divide fractions
Name an angle as acute, right, obtuse, or straight
Find the perimeter of any polygon
Give the reciprocal of any fraction
Convert a measure to different units with a unit multiplier

The procedures

Fractions

Adding or subtracting: rewrite over a common denominator first, then work the tops.
Multiplying: straight across, top times top and bottom times bottom.
Dividing: multiply by the reciprocal of the second fraction.

Unit multipliers

Write the conversion you know as a fraction that equals one, for example twelve inches over one foot.
Choose the arrangement whose bottom unit matches the unit you are cancelling.
Multiply, cancel the matching units, and the unit you wanted is what is left.

Angles

Acute is less than ninety degrees, right is exactly ninety.
Obtuse is between ninety and one hundred eighty; straight is exactly one hundred eighty.
The little square in a corner always means a right angle.

Perimeter

Perimeter is the distance around: add every side, no exceptions.
All sides must be in the same unit before you add.
If a side is unlabeled, the figure tells you: opposite sides of a rectangle match.

Worked

WORKED

Add 38 + 56.
The common denominator is 24.
That makes 924 + 2024.
ANSWER: 2924

WORKED

A rectangle is 12 units long and 7 units wide. Find its perimeter.
Two sides of 12 and two sides of 7.
12 + 7 + 12 + 7.
ANSWER: 38 units

Terms

Term	Meaning
perimeter	the distance around a figure, every side added
reciprocal	the fraction flipped over; a number times its reciprocal is one
right angle	an angle of exactly ninety degrees

Check yourself

1. Subtract: 56 − 14

2. Give the reciprocal of 94

3. A triangle has sides 9, 12, and 15. Find the perimeter.

reveal answers

712 · 49 · 36

This page is the summary, not the lesson. The full working, every step of every example, is on the board in class. Come here to remember what the week was about. Go there to learn how it is done.