Ext 6-8 Sampler

51 Grade8 IntegersModeledonaNumber Line Lesson17, 8ETeacherGuide 53 Objective48: To relatepositive andnegative integers to a horizontal number line. Toorder and compare integers. Materials: Algebra tiles, or black andwhite interlocking cubes (orpositive andnegative integer squares fromMaster 20),NumberLines (Master 22), thermometer Vocabulary: integers Positive andNegativeNumbers on a Number Line Display aFahrenheit thermometer and tenblack cubes (or integer squares). Eachblack square represents a positivenumber.Whatnumber is shown? (+10) What temperatureona thermometer is associatedwithpositive 10? (10degrees above zero) Using anumber line cut fromMaster 22, arrange the cubes in a straight line from0 to10. Thenmove the number line and cubes into the vertical position. Display10white cubes (or squares). Eachwhite cube represents anegativenumber.Whatnumber is shown? (–10) What temperature is related to–10? (10degrees below zero)Display a second cut out number linewith white cubes in a straight line to the left of 0. Draw anewnumber lineon theboard in thehorizontal positionwith thepositivenumbers going to the right and thenegativenumbers going to the left. Whichdirection shows thepositivenumbers? (right) Whichdirection shows thenegativenumbers? (left) Ask students if they can thinkof other examples of positive andnegativenumbers, e.g. heights above and below sea level, gains and losses on a football field, stock price gains and losses. Ordering andComparing Integers Thenumber lineon theboard represents the set of integers.The set of integers includes0andall positive andnegativenumbers. Showhowbraces areused to list the set of integers: I= {…–3, –2, –1, 0, +1, +2, +3…} 0 1 2 3 4 5 6 7 8 9 10 – + 0 - 10 - 9 - 8 - 7 - 6 - 5 - 4 - 3 - 2 - 1 1 2 3 4 5 6 7 8 9 10 Suppose the temperature inDetroitwas5° belowzero in themorningand10° abovezeroatnoon. Useblack and white cubes todisplay the two temperatures (10black cubes and5white cubes) andmove from–5 to+10 so they see the amount of change. Howdoes thenoon temperature compare to themorning temperature? (15°warmer) Writeon theboard: –5<10 Read the illustration together at the topof thepage. Emphasize that the values of numbers increase as youmove to the right anddecrease as youmove to the left.Work problems 3, 5 and9with the class.Have students complete thepageon their ownorwith apartner. Skill Builders 48-2, 48-4, 48-7, 49-2 - 53 ©Math TeachersPress, Inc.,Reproduction by anymeans is strictly prohibited. IntegersModeledon aNumber Line A thermometer turned sideways becomes anumber line showing the set of integers. Thewhite squares can be thought of as being to the left of the zeroon the number line. = – 3 Theblack squares can be thought of as being to the right of zero on the number line. = + 3 Drawblackorwhitesquareson thenumber line to showeachnumber. 1. + 5 2. – 4 Order the integers from least togreatest. Compare the integers.Use >,<,or =. 3. – 1, 0, 3, – 2, 1 ______ ______ ______ ______ ______ 4. 5, – 3, – 2, 0, 4 ______ ______ ______ ______ ______ 11. The temperature at noonwas 10° above zero. By 10 p.m., the temperature had dropped15°.What was the temperatureat 10 p.m.? ____________ – 3 – 2 – 1 0 + 1 + 2 + 3 – 3 – 2 – 1 0 + 1 + 2 + 3 – 5 – 4 – 3 – 2 – 1 0 + 1 + 2 + 3 + 4 + 5 – 5 – 4 – 3 – 2 – 1 0 + 1 + 2 + 3 + 4 + 5 5. 6. 7. 8. + 4 – 6 – 5 + 5 – 3 0 – 6 – 4 9. The temperature at noonwas 10°. The temperature at midnight was – 5°. What was the change in temperature? ____________ 10. A bird is flying 10 yards above sea level. A fish is swimming 20 yards below sea level. What is the distance between the bird and the fish? ____________ 12. The temperature at midnight was 10° below zero. At noon the next day, the temperaturewas 20° above zero. Howmany degrees had the temperature increased? ____________ – 2 – 1 – 3 – 2 0 > < -15° or 15° colder – 5° 30 yds. 30° < < 4 5 0 1 3 6.NS.6.c, 6.NS.7