Number Sense Workbook 7, Part 1: Unit 3

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1 Number Sense Workbook, Part : Unit Worksheet NS- page. a),, : 0,,,,, 0, : 0,, 0,, 0,, 0. a) Yes No Yes; Yes; Yes. a) 0 All whole numbers, since any whole number times zero is zero.. is a factor of. is a factor of 0. d) is not a factor of. INVESTIGATION A.,, 0,, d), e) 0, f) g) h) i) j) 0 k) l) -- m) B. The largest factor of any number n is n since dividing by anything larger than n won t result in a whole number. C. a),,,,, Yes. a) 0, 0, 0 No No d) 0 e) 0. a) 0,,,. a) 0,,,,,,,, All whole numbers have as a factor (since divides evenly into all numbers).. a) Any number n. No. All numbers are factors of 0 since any number times 0 is 0.. a) is a factor of. is a factor of every number. is a factor of. d) Every number has itself as a factor. e) is a factor of 0. f) Every number is a factor of a) is a multiple of. 0 is a multiple of. Any non-zero multiple of is at least. d) Any non-zero multiple of a number is at least that number. e) is a multiple of. f) Any number is a multiple of itself. Worksheet NS-0 page. a) Since 0 is the largest possible factor of 0. 0 is not a factor of 0 (or of any number).. a) st nd - - st nd st nd a) Cross out (,) and (,). Cross out (,) and (,). Cross out (,).. a) Connor notices that, as the st column increases, the nd column decreases. Since isn t a factor of and (,) would be the next pair (,), all factor pairs are listed already.. Any remaining pairs of factors would be ones that he has already but in reverse order.. a) st nd st nd st nd - - d) st nd e) st nd f) st nd g) st nd - - All whole numbers are factors of themselves. - -

2 Number Sense Workbook, Part : Unit (continued) g) continued h) st nd i) st nd - - j) st nd - - k) st nd l) st nd m) st nd n) st nd For : For : For : 0. Factor rainbows should include a),,,,,,,,,,, d),,, e), f),,,,,,, g),,,,,,,. a) Yes,,,, It gets smaller. d),,,,,,,,,, These are not all of the factors, e.g. = (the products of factors are also factors: = ). 0. Since is an even number, is the next smallest factor and the second largest factor is =. Worksheet NS- page.. Teacher to check.. a) 0, 0,, d), e), f),. a) (the first common multiple) =. a),,, 0. a) 0 d) e). 0 d) e) 0 f) g) h) i) 0 j) k) 0 l) 0 m) n). a),,,, 0, 0,,,,,, d),,, e),,,,,,, NOTE: You can stop dividing once you ve divided by a factor that s at least half the number.. a) d) e) f) g) h) 0. a) i) 0:,,, 0 :,,, ii), iii) GCF = i) :,,,,, :,,,,,,, ii),,, iii) GCF = i) 0:,,,, 0, 0 0:,,,,, 0,, 0 ii),,, 0 iii) GCF = 0

3 Number Sense Workbook, Part : Unit (continued) d) i) :,,,,, :,,,,,,, ii),,, iii) GCF =. a) ii) :, :,,, GCF = iii) :,,, 0:,,,,, 0,, 0 GCF = iv) 0:,,, 0 0:,,, 0,, 0 GCF = 0 GCF = a INVESTIGATION A. 0:,,,, 0, 0 :,,, GCF = :,,, :,, GCF = d) :,,, :,,,,,,,, GCF = B. GCF = INVESTIGATION A. a) GCF = LCM = = GCF = LCM = 0 =0 GCF = LCM = = d) GCF = LCM = 0 0 = 0 e) GCF = LCM = 0 0 = 0 f) GCF = LCM = = g) GCF = LCM = 0 = 0 h) GCF = LCM = = B. Circle: a),, f) and g) C. GCF = Worksheet NS- page. Teacher to check drawings the factors in each case are: a),,,,,, d), e),,, f),,.,.,. No, since a prime number is only divisible by itself and.. a) Teacher to check.,,,,. Teacher to check ( by ).. Teacher to check ( by 0 and by )..,,,,,,,,, 00. d) 0 e) 0. a) Yes Since <, their squares will have the same relationship.. a),,,, 0,,. a),,, 0,, 0,,,. a) 0 0 d). d) e) f) 0 g) h). 0 d) e) f) g) h) 0. d) 0 e) n. a) cm mm 0 km. a) The square with area cm has sides of length cm; the other has sides of cm. >. a),,,,,,,, 00,,, 00,, +,, 00 Worksheet NS- page. a) White circle Shaded triangle Small striped square d) Large white square. a) American football Bicycle, tricycle thing, bcjxp d) Who s there?, No way!. Because a banana is not a vehicle.. a) No, since is not even, it can be paired with any letter. (,R), (J,), (C,). a) (E,), (U,), (D,) True True d) (r,) (j, ) e) True f) (r,), (D,), (j,) g) True h) True i) (E,), (U,), (D,) j) True. Answers will vary (though generally easier to prove it false with a counter-example).. a) C B A F D E. Answers will vary for the counter-examples. Teacher to check. a) Reverse: people, boys Reverse: fruit, banana Reverse: animals that live in the water, fish

4 Number Sense Workbook, Part : Unit (continued) d) Reverse: start with a capital letter, form a sentence. Statement is false. Reverse (all red fruits are apples) is also false. Statement is false. Reverse (all soccer players are girls) is also false. d) Statement is true. Reverse (all shapes are circles) is false. e) Statement is true. Reverse (all toonies are Canadian coins worth $) is also true. Worksheet NS- page INVESTIGATION A. Are all whole numbers with ones digit 0 divisible by 0? B. Teacher to check. C D.,,,, n E. Yes. INVESTIGATION A. 0 B. n INVESTIGATION A. 0 B. 0 R R R R 0 R R R. a) Reverse: Any number that is divisible by has ones digit divisible by ,,,, is a repeating pattern d) Yes. a) Any number that is divisible by has ones digit divisible by. No; sample counterexample:. a) The statement is false. The reverse is also false: Any number divisible by has ones digit divisible by. The statement is true. The reverse is true: Any number divisible by has ones digit divisible by.. a) The ones digit will be 0,,,, or. The ones digit will be either or 0. The ones digit will be 0.. Circle:,,,,,, 0. Circle:, 0, 0,,,. Underline: 0, 0 Worksheet NS- page. Teacher to check... Teacher to check.. a) Yes since = 0. Yes.. a) + is a multiple of so it will have no remainder. d) i) ii) iii) iv) v) vi) 0. Since + = is a multiple of.. a) R R R d) R e) 000 R 0 f) R. a). a) Yes, since is a multiple of. Because is a multiple of. d) Both and are divisible by. 0. No, it will have a remainder of since has a remainder of.. + = and = R 0 Check: = R 0 + = and = R Check: = R. a) : = and = R : = and = R : = and = R No; any possible rearrangement will still have a sum of (and therefore a remainder of ).. If the sum of the digits of a number is divisible by, the number itself is divisible by.. a) Looking at the box on top of the page, we can see that,,, etc. are also multiples of so the same rule applies as for. If the sum of the digits of a number is divisible by, the number itself is divisible by.. a) 0 0 The part for numbers that are only divisible by since all numbers divisible by are also divisible by.

5 Number Sense Workbook, Part : Unit (continued). a), Outside the circles:,,,,,,,,, They are in the intersection part since any number divisible by both and will also be divisible by. A number is divisible by if it s even and the sum of its digits is divisible by. d) Circle:, Worksheet NS- page. a) ii) ; ; iii) 0; 0; 0 Yes. ; No 0; Yes d) ; No e) ; No f) ; Yes g) ; No h) ; No. If the last digits of a number form a number which is divisible by, then we can write it as a sum of a term divisible by 00 and a term divisible by. Sums of numbers both divisible by are divisible by.. a) Yes, any number ending in zeros is a multiple of 000. If the last digits of a number are divisible by, then we can write it as a sum of a term divisible by 000 and a term divisible by. Sums of numbers both divisible by are divisible by. ; Yes 0; Yes d) ; No e) ; No f) ; Yes. ; No d) 00, ; No e) 00, ; Yes f) 00, ; Yes Worksheet NS- page 0. a) # Factors,,,,,,,,,,,,,, 0,,, 0,,,,,,,,,,,,,,,,,,,,,,,, 0,,,, 0, 0,,,,,, and ; prime numbers d),, e) Gaps: Pattern:,,, f) They are perfect squares. g) ; square of = so, to be divisible by, + x must be divisible by. Possible values:,,. Circle:,,,, 0. a) Yes: + + = and = so both are divisible by. Yes: = and = so both are divisible by.. a) 0 0. a) Yes, it s even. No, the last digit is not 0 or. d) No, the last digit is not 0. e) No, none of the digits are 0.. = =. a) i) and iv) Answers will vary. Sample: i) ii) iii) iv) 0 v) Answers will vary. Samples: a) = So is divisible by. 0. In days. books ($0). = = GCF of and = = So the largest squares are mm mm.. a) True False; 0 is a counter example Worksheet NS- page. a). a) d). Teacher to check.., ;. Teacher to check.. a) The total number of pieces in a pie. The number of parts of the pie that are shaded in.. a) Yes. a) Pentagons 0 0 d) Triangles e) 0 f) 0

6 Number Sense Workbook, Part : Unit (continued). a) f).,, g),, 0.,. a) An Pl.,, B G S Worksheet NS- page.. a),,,, d). Teacher to check.. Teacher to check.... Teacher to check.. Teacher to check.. because third sized pieces are larger than quarter sized pieces.. a) No: < Yes: > Yes: > Worksheet NS- page. a) = 0 = 0 = 0 d) = e) = f) =. Teacher to check shading. a). Teacher to check shading. a). You divide into to find out that there are whole pies ( = R).. a) d) e) f). d) e) f). a). a) 0. a) d) e).. d),,. R; R; d) e) f) g) h) i). =. = Worksheet NS- page.. a) ; of =, ; of =, ; of = d) of 0 = e) of =. Teacher to check.. Teacher to check. Worksheet NS-0 page. a) d) e) d). Teacher to check pictures. a).. a). a) d) e) f). a). a),,, 0 d), e),.. 0,.

7 Number Sense Workbook, Part : Unit (continued) 0.. :. a) Worksheet NS- page e) f). of a year There are none left. Worksheet NS- page. 0. The fraction with the greater numerator... The greater fraction is the one with the smaller denominator.. a),,,,,,, d) 0, 0, 0, 0 e),, f),,,,,,,,,. a). a),,, since >. ; ; ; 0 ; ;,,,,,,,,,, d) The improper and mixed fractions represent the same total amount of parts. 0. Teacher to check.., since is closer to than to 0.. Teacher to check. 0,,,,, Compared them by looking at the relative sizes of the numerators and denominators. Worksheet NS- page. = < d) = e) < f) >. = and 0 =..,,.,,. d) 0. a) d) e) f) 0 g) h). a),,, 0,,,,,,,. a) Sample:, 0 ; so > since > 0. Sample:, 0 ; so > since > 0. Yes. a),,, 0,,. > > d) < e) > f) > g) >. a),,,,,,,, 0,, >. 0 d) g) h) 0.,,,,,,, Worksheet NS- page. a) 0 Blue White. Teacher to check... Teacher to check.. a), 0 0,,. Two of:,,. Five of:,,,, 0,,,,, 0 0, Worksheet NS- page.. + = ; + =. a) d) e) 0 f) g)

8 Number Sense Workbook, Part : Unit (continued) h). a). a) d) e) f) g) h). a) INVESTIGATION A. + ; it is larger B. ; there are pieces in each but eighth sized pieces are larger d) LCD = ;, e) LCD = ;, f) LCD = ;, g) LCD = 0;, h) LCD = ;,. a) 0 d) e) f) g) h) i). a) d) e) f) j), no. d) e) f) g) h). 0 = 0 = d) = e) 0 = f) 0 = g) 0 = h) = Worksheet NS- page. a). k) l) 0. a) ii) iii) iv) v) vi) 0 vii) viii) ii) iii) iv) v) vi) i) ii) iii) 0 iv) v) C. No, since according to A and B we know that: + < < + INVESTIGATION A.,,, ;, B.,, C. + = + and + =, so + = g) h) i) 0 0 Worksheet NS- page 0., yes, yes d), no e), no f), yes g), yes d). d) e) 0 f) g) h) i) vi). a) ii) iii) iv) ii) iii) iv) 0 ii) iii). LCD = ;, h), no j) iv) LCD = 0;, i), yes

9 Number Sense Workbook, Part : Unit (continued). d) e), f),... a) True, in this case you can always divide both the numerator and denominator by. e) 0 f) g) h) 0. km. kg. m... a) 0. False; e.g. False; e.g.. No, since the whole numbers are different you don t need to consider the fraction pieces ( > ). Worksheet NS-0 page. a), ;,, ;. a),, ;,, ;,, ;. a) 0 d).. a),,,, ; d) Worksheet NS- page. a) 0 d). of her money: $.0. Teacher to check. 0. Teacher to check.. She simply added the numerators together and the denominators together, rather than finding a common denominator first.... Sadia. No. a) hr = min = minutes. a) d) e)

Number Sense Workbook 3, Part 2

Number Sense Workbook 3, Part 2 Number Sense Workbook, Part page 1 Worksheet NS-1 page 0 1. a) 1st 7th c) 9th d) th e) f) g) 7 h). a) Ali Sam c) th d) e) Ashley is in th position. f) 17 = 1. a) Numbers marked with an X: 9, 11, 1, 1,