Adding and Subtracting Rational Numbers

Adding and Subtracting Rational Numbers

1.1 Rational Numbers 1.2 Adding Integers 1.3 Adding Rational Numbers 1.4 Subtracting Integers 1.5 Subtracting Rational Numbers

Chapter Learning Target: Understand adding and subtracting rational numbers.

Chapter Success Criteria: I can represent rational numbers on a

number line. I can explain the rules for adding and

subtracting integers using absolute value. I can apply addition and subtraction

with rational numbers to model real-life problems. I can solve problems involving addition and subtraction of rational numbers.

STEAM Video: "Freezing Solid"

STEAM Video

Freezing Solid

The Celsius temperature scale is defined using the freezing point, 0?C, and the boiling point, 100?C, of water. Why do you think the scale is defined using these two points?

Watch the STEAM Video "Freezing Solid." Then answer the following questions.

1. In the video, Tony says that the freezing point of wax is 53?C and the boiling point of wax is 343?C.

a. Describe the temperature of wax that has just changed from liquid form to solid form. Explain your reasoning.

b. After Tony blows out the candle, he demonstrates that there is still gas in the smoke. What do you know about the temperature of the gas that is in the smoke?

c. In what form is wax when the temperature is at 100?C, the boiling point of water?

2. Consider wax in solid, liquid, and gaseous forms. Which is hottest? coldest?

Performance Task

Melting Matters

Performance Task Name __________________________________(_c_o_n_ti_n_u_e_d_) ______________

Chapter

Date _________

1 Me4l.tiDnddrregyygiriMcceeeesatiosCtctferaelesrrebiuzsosendldioqieousxiditdhmee eitnercmauprsyeorltaihdtaustrteiastoeaf.ttIrhtoseofmmreeetrezcmiunrpgyeprnaoetieundrteit,soo?dr7r2o82p.5??C?C. .HYoowumusaeny

After completing this chapter, you will be able to use the concepts you learned to answer the questions in the STEAM Video Performance Task. You will answer questions using the melting points of the substances below.

1 Performance Task 5. Hpoo6iw.ntTd?1EiohnE8aeesxtsthcptAaolhtalBneAdirnteiesmaggssreticeIodltts3tieneics.mn?amoPgsEpOfelpeaxirMn2rcotdptae.eaieltaBn.amrtuuWthWioreneoe:ooal.hhftckMneiii1hnmcvcoA.hghemedaursprGsneegcuruodllreuubtbiiaincnrstssnpeyotttgtgha?mar1cnndRpe0pocceaote,eemedhTcira2'nehahphstbl0thtaoteayum1LmaWfasfrrr0tbiteseMeeotefd.lhhaoel.lmmeitttWteeffoiieeGfnspnCniehlchicogelgClrNtrhdlitioeArasuoegtoopaip?awehndlshEncfcteoodemtrueHeenotosaiiesghsrstnna.lnteoPeote7tupTMaatthzwtmn_lBtnbmEiaMooieaetienesoS_stnensaeeecrtsfl_etuwcgrarcalatairattscla_ncubIrnhihowptucttnncr_sehistoeyyrwegucat_eeeyioosahxmsns_aprfuntttctsao_bhs?achtauioe_?esaenwsisrro9_nttieumas3?lcl3?_g?biiyae2dn.boe1W_s9M2b2'eofmt1_s5ba?s3ar.ehi?4oCt_1oenm1leLli.3icl3mdt_cc.1tnuia9eoe8o0iehn_gt6bflrm.ntetfg_8c2eshiew0nh3eu_tlverPhsgaboaee_meonlsnaraC_putkigcteoano_elhetlipnist_etqnyicfpm(_utnrrte?oio?ogi_gCpdihhms_ne)ptaoitr_?osslasw_viotcBtnue_hilaittgire_lhpdelI_erslditood.et_oAsbwaHl_allslseire_ouiqmLsgmw_beuthe_asstislddrt_tnaaoiri_oebnnnsrto_ggche,euf_repLrvt_iooLerm_Cmdinm._etll_.eitlqiI_tnnui_gniE_dgpx_tope_oiorn_csitn_iosst_l?esi_dsc?_1o_?Tm_6hp_,eau_rsseteattoeDsate __________ ACllorpigyhrtigshrte?seBrviegdI.deas Learning, LLC

Ice Beeswax Mercury Plastic

Tin Ethanol Acetone Chocolate

You will graph the melting points of the substances on a number line to make comparisons. How is the freezing point of a substance related to its melting point? What is meant when someone says it is below freezing outside? Explain.

Big Ideas Math: ModelingARsesaelsLsimfeenGtrBadooek7

17

1

Getting Ready for Chapter

Chapter Exploration

1. Work with a partner. Plot and connect the points to make a picture.

1(1, 11) 6(15, 5) 11(11, 1) 16(0, 0) 21(-9, -6) 26(-9, -11) 31(-17, -10) 36(-8, 2) 41(-2, 12)

2(4, 10) 7(15, 3) 12(9, 2) 17(3, 1) 22(-9, -7) 27(-11, -10) 32(-15, -7) 37(-5, 6)

3(7, 10) 8(16, 1) 13(7, 1) 18(1, 1) 23(-7, -9) 28(-13, -11) 33(-12, -6) 38(-3, 9)

y 12

4(11, 9) 9(16, -1) 14(5, -1) 19(-2, 0) 24(-7, -11) 29(-15, -11) 34(-11, -6) 39(-4, 10)

5(13, 8) 10(15, -1) 15(1, -1) 20(-6, -2) 25(-8, -12) 30(-17, -12) 35(-10, -3) 40(-5, 10)

10

8

6

4

2

-18 -16 -14 -12 -10 -8 -6 -4 -2 O -2 -4 -6 -8

-10 -12

2 4 6 8 10 12 14 16 18 x

2. Create your own "dot-to-dot" picture. Use at least 20 points.

Vocabulary

The following vocabulary terms are defined in this chapter. Think about what each term might mean and record your thoughts.

integers

absolute value

rational number

additive inverse

2

1.1 Rational Numbers

Learning Target: Understand absolute values and ordering of rational numbers.

Success Criteria: ? I can graph rational numbers on a number line. ? I can find the absolute value of a rational number. ? I can use a number line to compare rational numbers.

Recall that integers are the set of whole numbers and their opposites.

A rational number is a number that can be written as --a, where a and b are

b

integers and b 0.

EXPLORATION 1

Using a Number Line

Work with a partner. Make a number line on the floor. Include both negative numbers and positive numbers.

a. Stand on an integer. Then have your partner stand on the opposite of the integer. How far are each of you from 0? What do you call the distance between a number and 0 on a number line?

b. Stand on a rational number that is not an integer. Then have your partner stand on any other number. Which number is greater? How do you know?

Math Practice

Find Entry Points What are some ways to determine which of two numbers is greater?

c. Stand on any number other than 0 on the number line. Can your partner stand on a number that is: ? greater than your number and farther from 0?

? greater than your number and closer to 0?

? less than your number and the same distance from 0?

? less than your number and farther from 0?

For each case in which it was not possible to stand on a number as directed, explain why it is not possible. In each of the other cases, how can you decide where your partner can stand?

Section 1.1 Rational Numbers

3

1.1 Lesson

Key Vocabulary integers, p. 3 rational number, p. 3 absolute value, p. 4

Key Idea

Absolute Value Words The absolute value of a number is the distance between the

number and 0 on a number line. The absolute value of a number

a is written as a .

4 units

4 units

-5 -4 -3 -2 -1 0 1 2 3 4 5

Numbers

-4 = 4

4 = 4

EXAMPLE 1 Finding Absolute Values of Rational Numbers

a. Find the absolute value of -3.

Graph -3 on a number line.

-6 -5 -4 -3 -2 -1 3

So, -3 = 3.

b. Find the absolute value of 1--1.

4

0

1

2

The distance between -3 and 0 is 3.

Graph

1

1 4

on

a

number

line.

-1

1 2

-1

-

1 2

0

1 2

1

1

1 2

2

2

1 2

1

1 4

The

distance

between

1

1 4

and

0

is

1

1 4

.

So, 1--1 = 1--1.

4

4

Try It Find the absolute value.

1. 7

2. ---5 3

3. -2.6

4

Chapter 1 Adding and Subtracting Rational Numbers

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