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Lab 4 Related Related number number sentences sentences 7 4 6 12 5 2 10 1 9 Algebra 3 8 20 1 Complete using the numbers above. a 7+4= d 12 ÷ 3 = +1 b9–3=5+ –1 e 12 ÷ 6 = π1 c 8π = 20 – 4 f 20 + =3π 2 Write as many expressions as you can using the numbers. There must be two numbers and an operations sign (+, –, ÷, π) on each side of the = (is equal to). 120 ! = = = = = = = = = = = = = = ACMNA082 & ACMNA083 Patterns and algebra • Solve word problems by using number sentences involving multiplication or division where there is no remainder. • Use equivalent number sentences involving addition and subtraction to find unknown quantities. Missing Missing values values Algebra 1 Complete these sequences. a 1.10 1.11 1.12 b 2! 3! 4! c 0.1 0.3 0.5 d 0.97 0.96 0.95 e 5! 5@ 5# 2 True or false. a 6+8=8+6 _____________ b 4 π 9 = 9 π 4 _____________ c 12 ÷ 4 = 4 ÷ 12 _____________ d 16 – 5 = 5 – 16 _____________ e 3π2π7=2π7π3 _____________ f 6 + 8 + 4 = 4 + 7 + 8 _____________ g 12 ÷ 6 ÷ 2 = 6 ÷ 2 ÷ 12 _____________ h 16 + 7 + 3 = 13 + 17 + 6 _____________ i 36 π 10 = 10 π 36 _____________ j 3 π 17 π 0 = 6 π 0 π 14 _____________ k 27 + 12 + 13 = 12 + 27 + 13 _____________ l 3 π 2 + 6 = 3 π 6 + 2 3 a 7π = 28 b = _______ = _______ = 50 = 16 + 36 j ÷9=9 g 56 = 4 π = _______ Challenge! – 6 = 14 d k 100 – π7 h 71 = l 72 + 36 = = _______ = _______ – 29 = _______ = 37 o 100 ÷ 2 ÷ + 18 = 40 = _______ = _______ = _______ n =6 = _______ = _______ = _______ m4+7+ c 42 ÷ = _______ f 49 = e 15 = 30 ÷ i 2π – 6 = 11 _____________ = _______ =5 p3π7π2= = _______ = _______ Find the value of the star in each. a 36 + 52 = 100 – 51 + b π4÷5= –2 ACMNA082 & ACMNA083 Patterns and algebra • Solve word problems by using number sentences involving multiplication or division where there is no remainder. • Use equivalent number sentences involving addition and subtraction to find unknown quantities. ! 121 = = Equal Equal terms terms 1 Use = or =. a 4 π 3 _______ 6 π 2 means ‘is equal to’. b 8 + 7 _______ 9 + 6 Number patterns means ‘is not equal to’. c 4 π 6 _______ 3 π 7 d 16 – 9 _______ 8 – 1 e 9 π 3 _______ 7 π 4 f 16 ÷ 4 _______ 35 ÷ 7 g 64 ÷ 8 _______ 56 ÷ 7 h 100 – 36 _______ 8 π 8 i 5 + 17 _______ 33 – 12 j 8 + 8 _______ 8 π 2 k 7 + 7 _______ 7 π 7 l 42 + 14 _______ 8 π 7 m 50 – 16 _______ 7 π 5 n 72 ÷ 8 _______ 12 – 3 2 a Look at the pattern to complete the table. Order of term 1 2 Term 1 3 3 4 5 6 7 8 4 5 6 7 8 b Draw the 10th term. c Describe the pattern. 3 a Look at the pattern to complete the table. Order of term 1 2 3 Term 2 4 6 b Draw the 12th term. c Describe the pattern. 4 Draw your own pattern, then complete the table. Order of term 1 2 3 4 5 6 7 8 Term 122 ! ACMNA081, ACMNA082 & ACMNA083 Patterns and algebra • Explore and describe number patterns resulting from performing multiplication. • Solve word problems by using number sentences involving multiplication or division where there is no remainder. • Use equivalent number sentences involving addition and subtraction to find unknown quantities. Addition Addition and and multiplication multiplication patterns patterns Strategies 1 a 2 + 3 + 8 =______ b 7 + 4 + 6 =______ c 9 + 2 + 5 =______ d 8 + 5 + 1 =______ 3 + 2 + 8 =______ 4 + 6 + 7 =______ 5 + 2 + 9 =______ 1 + 8 + 5 =______ 8 + 3 + 2 =______ 6 + 4 + 7 =______ 2 + 9 + 5 =______ 1 + 5 + 8 =______ e 9 + 7 + 11 =______ f 8 + 7 + 13 =______ g 16 + 8 + 4 =______ h 15 + 7 + 9 =______ 11 + 9 + 7 =______ 13 + 8 + 7 =______ 8 + 16 + 4 =______ 7 + 9 + 15 =______ 7 + 11 + 9 =______ 8 + 13 + 7 =______ 8 + 4 + 16 =______ 9 + 15 + 7 =______ 2 Write the rule about adding numbers. _________________________________________________________________________________________________________ 3 a 2 π 3 π 4 =______ b 7 π 2 π 3 =______ c 5 π 7 π 2 =______ d 9 π 4 π 5 =______ 4 π 2 π 3 =______ 2 π 3 π 7 =______ 7 π 5 π 2 =______ 5 π 9 π 4 =______ 3 π 4 π 2 =______ 2 π 7 π 3 =______ 2 π 5 π 7 =______ 4 π 5 π 9 =______ f 9 π 6 π 10 =______ g 4 π 8 π 2 =______ h 3 π 9 π 7 =______ e 6 π 8 π 5 =______ 5 π 8 π 6 =______ 10 π 6 π 9 =______ 8 π 2 π 4 =______ 9 π 7 π 3 =______ 5 π 6 π 8 =______ 9 π 10 π 6 =______ 2 π 4 π 8 =______ 3 π 7 π 9 =______ 4 Write the rule about multiplying numbers. _________________________________________________________________________________________________________ 5 In question 3 circle the easiest multiplication in each group. 6 These numbers have to be added. Circle the numbers you would add first. a d g j 16 15 14 8 15 5 51 68 49 b e h 7 9 13 12 6 4 22 18 36 c f i 11 9 17 27 17 13 43 19 31 Why did you choose those numbers? _________________________________________________________ _____________________________________________________________________________________________________ 7 Work the answers mentally for question 6. a ________ b ________ c ________ d ________ e ________ f ________ g ________ h ________ i ________ ACMNA082 & ACMNA083 Patterns and algebra • Solve word problems by using number sentences involving multiplication or division where there is no remainder. • Use equivalent number sentences involving addition and subtraction to find unknown quantities. ! 123