Grade FG Square Triangular Cube Numbers Recognise and
Grade F/G Square, Triangular & Cube Numbers Recognise and use sequences of square, triangular and cube numbers, and simple arithmetic sequences If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl. org. uk
Key Vocabulary Sequence Term Square number Triangular number Cube number Arithmetic sequence
Square Numbers Here are the first 5 square numbers. 1, 4, 9, 16, 25 This is how they work 1² = 1 x 1 = 1 2² = 2 x 2 = 4 3² = 3 x 3 = 9 4² = 4 x 4 = 16 5² = 5 x 5 = 25
Now you try: a) What is the first square number 81 (9² or 9 x 9) above 75? b) Which two square numbers have a 100 & 64 difference of 36? c) What is the 15 th square number? 15² = 15 x 15 = 225
Triangular Numbers Here are the first 5 triangular numbers. 1, 3, 6, 10, 15 +2 +3 This is how they work 1+2=3 1+2+3=6 1 + 2 + 3 + 4 = 10 1 + 2 + 3 + 4 + 5 = 15 +4 +5
Now you try: a) What is the 7 th triangular number? 28 b) Which two triangular numbers have a sum of 31? 10 & 21 c) What is the sum of the first 5 triangular numbers? 35
Cube Numbers Here are the first 5 cube numbers. 1, 8, 27, 64, 125 This is how they work 1³ = 1 x 1 = 1 2³ = 2 x 2 = 8 3³ = 3 x 3 = 27 4³ = 4 x 4 = 64 5³ = 5 x 5 = 125
Now you try: a) What is the first cube number 343 (7³ or 7 x 7) above 300? b) Which two cube numbers have a 216 & 125 difference of 91? c) What is the 9 th cube number? 9³ = 9 x 9 = 729
Problem Solving and Reasoning Which number greater than 1 is the first to appear in both the square numbers and triangular numbers? Solution Here are the first 10 square numbers 1, 4, 9, 16, 25, 36, 49, 64, 81, 100 Now let’s list out the triangular numbers 1, 3, 6, 10, 15, 21, 28, 36 +2 +3 +4 +5 +6 +7 +8 So the answer is 36.
Problem Solving and Reasoning Here are the first 5 cube numbers 1, 8, 27, 64, 125 Amy says; “If I add any two of these 5 numbers I will not get a prime number. ” Show that Amy is correct. 1 + 8 = 9 (multiple of 3) 1 + 27 = 28 (multiple of 2) 1 + 64 = 65 (multiple of 5) 1 + 125 = 126 (multiple of 2) 8 + 27 = 35 (multiple of 5) 8 + 64 = 72 (multiple of 2) 8 + 125 = 133 (multiple of 7, 7 x 19 = 133) 27 + 64 = 91 (multiple of 7, 7 x 13 = 91) 64 + 125 = 189 (multiple of 9, 9 x 21 = 189)
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