7th Grade Chapter 3
3-1 Rounding and Estimating
Estimation can be used to quickly verify whether calculated results are reasonable. There are several ways to estimate sums and differences, including rounding, front-end estimation, and clustering. There is no one right way to estimate. The kinds of numbers used and the situations in which an estimate is needed often determine which estimation technique makes sense to use. How close to the estimate needs to be will also influence the choice of method.
3-2 Estimating Decimal Products and Quotients
Rounding is an important step in estimating products. Choosing compatible numbers makes the process of estimating quotients easier. Using mental math and estimating can help students evaluate the reasonableness of the answers to their calculations.
3-3 Using Formulas
A formula is an open-sentence equation that shows a relationship between variables. Formulas relate quantities in the real world. You cannot use a formula to find a value of a variable unless the values of all other variables in the formula are known. Commonly used formulas include A=lw, P=2l +2w, or d=rt.
3-4/3-5 Solving Equations by
Adding/Subtracting/Multiplying/Dividing Decimals
The subtraction and addition properties of equality are used to solve equations involving decimals. The process for solving one-step linear equations is the same, using the properties of numbers and order of operations to rewrite the equations without grouping symbols and to collect like terms. The rules for addition and subtraction with decimals must also be followed. Decimal numbers must be added or subtracted with the place values aligned.
The division and multiplication properties of equality are used to solve one-step linear equations involving decimals. When dividing, multiply the dividend and the divisor by the same power of 10 so that the divisor is a whole number. Remind students that division by zero is undefined. Students should take care when multiplying to make sure that the number of places to the right of the decimal in the product ins equal to the sum of the number of places to the right of the decimal in the factors.
3-6 Using the Metric System
The standard system of measurement used by scientist around the world is known as the International System of Units (SI). SI units are easy to use because they are based on powers of 10. Each unit is ten times larger than the next smallest unit, and one-tenth the size of the next larger unit. The basic units are the meter, liter, and the gram. The meter is used to measure the length or the distance between two points. The distance from the floor to a doorknob is approximately one meter. The liter is used to measure the volume or capacity of a liquid. One liter is the approximate volume of a medium sized carton of milk. The gram is used to measure mass. One gram is approximately the mass of a paper clip.
3-7 Reasoning Strategy: Acting It Out
You can often solve a difficult math problem by considering the situation and acting it out. Before acting out the problem, analyze the problem and organize the given information. Then develop a plan for acting out the problem.