Number Sense AP Book 7, Part 2: Unit 1

Transcription

1 Number Sense AP Book, Part : Unit AP Book NS- page. A. 0. B C. 0. D. 0.0 E a) = 0. = 0. = 0. 0 = 0. 0 = 0. 0 = Teacher to check.. a) a) i) Numerators start at and increase by each time. Denominators start at and increase by each time. ii) Numerators start at and increase by each time. Denominators start at and increase by each time. i) 0. ii) 0.. a) Circle:,,,, 0 0, 0 00 All the fractions circled in part a) can be written in lower terms because the common factors in the numerator and denominator will cancel out. Circle: 0., 0., 0.0, 0.. These are the expected responses. Teacher to check explanations. a) Fraction Decimal Decimal Fraction AP Book NS- page. a). = = 0. = = 0. = =.. 0. = 0. 0.= =.. a) Start at 0.0 and add 0.0 each time. 0.0, 0., 0., 0., 0., 0., 0., 0., 0., 0., so so AP Book NS- page. a). a) Since =, = ( ) = ( ) Since =, = ( ) = ( ). a) g) h) i) j) = 0. = = 0. = = 0. = = 0. = = 0. = =. = =. = = 0. = = 0. 0 = 0 = 0.. a) 0., 0., 0. Add 0. each time. = 0.; = 0.; = 0.; = 0.; =. Check not shown. g) BONUS 0 = = 0. 0 = 0. = = = 0. AP Book NS- page. a) g) 0. h) 0. i). j).. Circle: 0., 0.. a) = 0.. a) 0.; 0. 0.; 0. Answer Keys for AP Book. U-

2 Number Sense AP Book, Part : Unit (continue. a) 0.; 0. 0.; ; ; 0.. A. 0.. B. 0. C. 0. D a) < > >. a) 0., 0., 0., 0.. a) 0., 0., 0., 0. 0., 0., 0., 0. 0., 0., 0., 0. 0., 0., 0., 0. 0., 0., 0., 0. AP Book NS- page = 0. = 0., = 0. = 0., = 0. = 0., = 0. = 0. = 0., = 0., = 0., = 0., = 0.. a) 0. 0.; closest to 0. 0.; closest to 0. 0.; closest to 0.. a) 0.00, 0.00, 0.; closest to 0., 0., 0.; closest to.00,.,.; closest to. Using long division, we can see that: 0.; 0.; 0.; = 0.. a) i),,, ii) iii) i) 0 < < 0 0 < 0 < < < ii) iii) Teacher to check.. a) 0.. Answers may vary. Sample solutions: a). a) ,,,, AP Book NS-0 page INVESTIGATION A. Answers will vary but the decimal expansions will all terminate. B. They can always be written as some integer divided by some power of, i.e., as a decimal fraction. C. a) terminates: repeats repeats repeats repeats terminates: D. 0 = 00 = E. Answers will vary but this type of fraction will always terminate. F. and are already in simplest form;,, Only terminates since it s the only one that reduces to a fraction whose denominator is a multiple of s &/or s.. a),,,,, They will repeat since their denominators can t be written as a product of s &/or s.. a),,,,,,,,,, Only, and will terminate: their denominators are products of s. 0.0, 0., 0., 0., 0., 0., 0., 0. 0., 0., 0. Only, and terminate, as predicted.. In each case, the numerator has a factor of so, in lowest terms, the denominators no longer have a factor of (since it cancels out). AP Book NS- page a) i) 0. ii) 0. iii) 0. U- Answer Keys for AP Book.

3 Number Sense AP Book, Part : Unit (continue i) ii) iii) 0. Teacher to check.. a) i) ii). iii). iv).. There s no place to start adding and carrying the s... a) i) ii) iii) iv) i) 0. ii) 0.0 iii) 0. iv) 0.0 AP Book NS- page. a) 0.0, 0., 0., 0. 0., 0., 0., 0., 0., 0.0, , 0., 0., a) Teacher to check. 0., 0., 0., a) a) a) = = =. a) 0.00 i) 0.0 ii) 0.00 iii) 0. iv) 0.0 v) vi) AP Book NS- page a) g) h) i) j). a) g) 0.0 h) 0.00 i) a) 0., 0., 0. Answers will vary but correct prediction is , like in a),, ,, ,, , = 0, 0 = 0 = g) = h) 00 i) 0 = 0 Answer Keys for AP Book. U-

4 Number Sense AP Book, Part : Unit (continue AP Book NS- page. a) 0 : 0, 0% : 0, %. a) 0% % % %. a) 0 : 0 : 0 : 0 : 0. a) 0 0 = 0% 0 = %. a) 0% % % % %. a) Teacher to check drawing. Fraction Percent % % % AP Book NS- page. Red: % Blue: 0%, + 0 = 0 0% of the grid is coloured.. a) = 0% = 0% = % = 0%. a) % % %. a) % % %. a) % : 0; % cents; % % % % AP Book NS- page. a). 0% white, 0% grey. a) Students should shade dots. 0%. 0% or 0 marbles. a) g) 0 0 = = 0. 0 = 0. 0 = = 0. 0 = = 0.0 h) 0 0 =.00. a) a) 0.0 g) 0.0 h) = 0% = 0 0 = 0% = 0 0 = 0% 0 = % 0 = % 0 = %. a) 0% 0% 0% % 0% % g) 0% h) % i) % j) %. a) % % % %. = 0% jazz, 0% rock AP Book NS- page. 0 0 = 0% 0 = % 0 = %. 0%. = 0 0 = 0% = 0 0 = 0% = 0 = % 0 = % g) h) 0 0 = 0% 0 0 = 0% 0 = % i) = 0 0 = 0%. a) 0. = % = 0. = 0% = 0. = 0% = 0. = 0% 00 = 0. = %. a) 0.0 = 0 0 = 0. = 0 = 0. = 0 = = 0 = = 0 0 =. a) % % 0% 0% 0% % g) %. a) a) % % % % U- Answer Keys for AP Book.

5 Number Sense AP Book, Part : Unit (continue % % AP Book NS- page. a) 0% % 0% 0% % 0% g) 0%. Teacher to check.. 0 = 0 0 = 0.0 = 0%. 0%, 0%, 0%, 0%, 0%. Teacher to check.. Teacher to check.. 0 0, 0%. 0, 0%, 0%. Teacher to check. AP Book NS- page. Fraction Decimal Percent % 0. % 0. % 0.0 0% 0.0 0% 0.0 0% 0. % 0. % 0 0. %. 0 0 < 0 < % 0 > 0 > % 0 > 0 0 > 0% 0 0 > 0 > % 0 < 0 0. < % g) 0 < < % h) = 0 = % i) 0 < 0 < % j) 0 = 0 0 = % k) 0 0 > 0 0. > % l) 0 > 0 0 > %. a) = 0., % = 0. %,, 0. = 0., 0% = 0., 0., 0% = 0., % = , %,. a) Drama Pepperoni AP Book NS-0 page. a) a) a).. =. % of =.. = % of. = =. % of =.. = 0 % of =.. =. % of 0. = = 0.. % 0. % 0 0% a) = = = 0.. a). a) % % % % % 0% % 0% a) 0. $. a) % of $0 = $; sale price is $0 % of $ = $.; sale price is $. AP Book NS- page. a) = % of is 0 0 =. % of is.. a).. Answer Keys for AP Book. U-

6 Number Sense AP Book, Part : Unit (continue g) 0. h).. a) i) 0 = = % of 0 is ii) % of 0 is % of 0 is % of 0 is + = Yes, the answer is the same regardless of the method used. Yes ; half of 0 Teacher to check explanation.. The answer is for both since (0 0) 0 = (0 0) 0. AP Book NS- page 0. is of : = : is of : = : is of : = :. : = : : = :. a) : 0 = : 0 = : 0 = : 0 =. =?? : = :? = 0 : 0 =? : 0 0 =?.? : 0 = : 0? 0 = 0 : =? : 0 =? 0 :? = : 0? = 0. part: whole:? percent: 0? = 0 0 part:? whole: percent:? = 0 part: whole:? percent:? = 0 part: whole: 0 percent:? 0 =? 0 part:? whole: percent:? = 0 g) part: whole: percent:? =? 0 AP Book NS- page. a) 0 g) h). a) a) 0 0. a) part: whole: 0 percent:?? 0 0? = 0 part: whole:? percent:? 0? = part:? whole: percent:? 0? =. part:? whole 0 percent:? 0 0? =. 0% g) 0. 0 =, so x = =. a) x ; x 0 0 x = 0 x ; x 0 0 x = x ; x x = 0. a)? = part:? whole: percent:? 0?? = part: whole: 0 percent:?? ;? ? = part:? whole: percent:? 0 ;?.? =. U- Answer Keys for AP Book.

7 Number Sense AP Book, Part : Unit (continue. In Q, we had to first choose appropriate equivalent ratios.. a) 0 0. % red % not red.. AP Book NS- page. b g c a) 0. b g c a) ; ;. Ron received or $0.. Subject E S Ella received or $. Time F P D M 0 % 0. % 0.0. a) $0. 00 students. a) fish. 0 stamps. 00 lights AP Book NS- page. a) % % %. Answers will vary teacher to check.. %. Item B P C. 0% Money spent F P $ 0 % $ 0% $ % $ ; ;. b:g b g %b %g a) : : : : : : g) : h) : i) : M F 0% % 0. AP Book NS- page.. a) boys boys. a) unit = beads 0 beads total unit = beads beads total unit = beads 0 beads total AP Book NS- page.. a) = = 0 = =. Item S B B RP $.00 $. $.0 D% % % 0% D$ $.0 $. $. SP $.0 $. $.. $ saved. chair: table: = % 0 = % sofa: = 0%. There are now sturgeon in the lake; 00.% of total.. s b g %b %g a) 0 0. a) boys; girls 0 boys; girls boys; girls boys; girls boys; girls boys; girls. a) Classroom A Classroom B. Models should include the following: a) 0 red; 0 green red; green. 0 fish. fish Teacher to check model. AP Book NS- page. a). a) 0... b. a),,,, = = = = Answer Keys for AP Book. U-

8 Number Sense AP Book, Part : Unit (continue INVESTIGATION A. i) ii) iii) iv) B. No ; ; 0 ; 0 ; INVESTIGATION A. i) ; = ii) ; = B. Yes AP Book NS- page... of = of = 0 = = = = 0 = = = 0 =. a b. a) g) h). No. a) (or ) = =. 0 (or 0 ). a c b d. a). a). a) Circle:, Circle:,,,, 0 AP Book NS-0 page. a) =,, =, =, a, a a, a b a, b a. a) = = = g) h). 0, 0 = 0, 0 = c b, bc a = c b a. = = c a b = c b a. a) = = g) 0 AP Book NS- page. (or ) cups. (or ) hours. people. 0 pieces. hours. of a pie. a) 0. a) 0 (or 0 ) cards 0 cards. 0 years old. years old AP Book NS- page., right;, right. a), 0, left i) 0.0 ii) 0.00 iii) iv) 0. v) 0.0 vi) a) 0.,,, left, left i) 0.00 ii) iii) iv) 0.0 v) 0.0 vi) 0.. a) less. a). 0.0,. 0.00, 0.0. a) ii) 0. iii) iv) 0.00 i),. ii), 00, iii), 0, 0.0 U- Answer Keys for AP Book.

9 Number Sense AP Book, Part : Unit (continue AP Book NS- page. a). a) 0.0 (or 0.) (or 0.) 0.0.,, 0. 0, 0, 0.0,, 0.. a), 0, 00, a) i) ii) 0 iii) 0 iv) v) 000 They are the same.. Teacher to check shading = 0 = 0 = 0. a) The # of zeros in the product = the total # of zeros in the denominators of the multiplied fractions. a) ii) 0. iii) 0. iv) 0.0 (or 0.00) v) 0.00 vi) The # of decimal places in the product = the total # of decimal places in the multiplied decimals 0. g) 0. h) 0.0 i) 0. j) Estimates may vary. Sample answers: a) = = = 0 = 0 0 = = 000. a) a) Correct as is Should be. Correct as is Correct as is. a).... Teacher to check. Sample answers: a = 0., b = ; a =, b = 0.; a =, b = 0.; a =, b = 0., etc...0 m.. L AP Book NS- page. a) cm, cm m, m m, m dm, dm m, m g) m, m h) dm, dm i) km, km. a) pennies, $. cm,. m The both deal with one unit that is a whole, and a second unit equal to 0 of the first.. It is equal to. m since there are 0 cm in m. AP Book NS- page 0. a) g) 00 h) 00 i) 000 j) 0 k) 000 l) = 0 + = 0 + = 0 + = 00 + = g) = h) = 0. a millimetre a millimetre a decimetre. dm cm cm mm mm g) mm h) mm i) m. 0 m = cm 0 0 dm = 0 mm m = 0 mm. m + m = m m = 00 cm + 0 cm = 0 cm dm cm mm mm. a),,,,,, 0, 0,, 0,, 0,,.. dm. cm. m. dm mm.. km. The cm are like the pennies since there are 0 of them in whole unit (i.e. m or dollars). Answer Keys for AP Book. U-

10 Number Sense AP Book, Part : Unit (continue. Combinations may vary.. Sample answers: a) or Tree Height (cm) White Birch 000 Lodgepole Pine 00 Western Red Cedar 00 Red Oak 00 In order from tallest to shortest: Western Red Cedar, Lodgepole Pine, Red Oak, White Birch U- Answer Keys for AP Book.