Algebra 1 Common Core Student Edition, Grade 8-9

9

The diagrams

sh o w o n e w ay

to look at the

problem .Try t o

think of other

ways you could

represent it.

Getting Ready!

An animal shelter has a fundraising goal o f $ 7 5 0 0. The diagram shows

t h e r e s u lt s f o r t h e f i r s t t h r e e w e e k s. T h e f i r s t a m o u n t is n e g a tiv e

due to upfront costs. W hen will th e sh elter reach its goal? M ake an

estim ate. S tate any assumptions and ju stify your reasoning.

MATHEMATICAL

PRACTICES

' : $7500 —$7500 —i-$7500

-$500+ $0 $500+[_J_$0

$1500+ -mm

czf!-$o

An Introduction

to Equations

@ Common Core State Standards

A-CED.A.1 Create equations and inequalities in one

variable and use them to solve problems.

MP 1, MP 3, MP 4, MP 6, MP 7, MP 8

Objective To solve equations using tables and m ental m ath

Lesson
Vocabulary
equat ion
open sentence
so l u t i o n o f an
equat ion

T h e p r o b le m i n th e S o lv e I t c a n b e m o d e le d b y a n e q u a t io n. A n equation is a

m a t h e m a t ic a l s e n te n c e t h a t u s e s a n e q u a l s ig n ( = ).

Esse n t i a l U n d e r st a n d i n g Y o u c a n u s e a n e q u a t io n t o r e p r e s e n t th e r e la t io n s h ip

b e t w e e n t w o q u a n t it ie s t h a t h a v e th e s a m e v a lu e.

A n e q u a t io n is t r u e i f th e e x p r e s s io n s o n e it h e r s id e o f th e e q u a l s ig n a re e q u a l

(1 + 1 = 2, x + x = 2x). A n e q u a tio n is fa ls e i f th e e x p re s s io n s o n e ith e r sid e o f th e e q u a l

s ig n a re n o t e q u a l (1 + 1 = 3, x + x = 3x). A n e q u a tio n is a n open sentence if it contains

o n e o r m o r e v a ria b le s a n d m a y b e tr u e o r fa ls e d e p e n d in g o n th e v a lu e s o f its v a ria b le s.

Plan

How do you classify

an equation?

If an equation contains

only numbers, simplify

the expressions on either

side to determine if they

are equal. If there is a

variable in the equation,

it is open.

Classifying Equations

Is the equation true, false, or open? Explain.

Q 2 4 + 18 = 2 0 + 2 2 True, because both expressions equal 42

0 7 • 8 = 5 4 False, because 7 • 8 = 56 and 56 54

G 2x - 14 = 5 4 Open, because there is a variable

& G o t It? 1. I s t h e e q u a t i o n true, false, or open? Explain.

a. 3y+6 = 5 y-8 b. 16 - 7 = 4 + 5 C. 32 -^8 = 2 • 3

c

PowerAlgebra.com | Lesson 1-8 An Introduct ion t o Equations^53

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