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Starting number sequences

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CONTENTS

ITEM TYPE NUMBER
Number sequences - 2 to 5 Workout 54 slides
Number sequences Library 0 questions
Once you have registered, you can work through the slides one by one. The workout comprises a series of sides that guide you systematically through the topic concept by concept, skill by skill. The slides may be used with or without the support of a tutor. The methodology is based on problem-solving that advances in logical succession by concept and difficulty. The student is presented with a problem or series of questions, and the next slide presents the fully-worked solution. To use the material you must sign-in or create an account. blacksacademy.net comprises a complete course in mathematics with resources that are comprehensive.

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SAMPLE FROM THE WORKOUT

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SLIDE 1 - TASK 1

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SLIDE 2 - TASK 2

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SAMPLE FROM THE LIBRARY

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QUESTION [difficulty 0.1]

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SOLUTION

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DEPENDENCIES

158: Addition and subtraction
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152: Starting number sequences
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154: Further number sequences part I

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CONCEPTS

ITEM
 LEV.
Fundamental sequence 1 to 10 304.1
Counting up and down in 10s 304.3
Counting up and down to 20 304.5
Counting in 2s, even sequence 304.7
Counting in 2s, odd sequence 304.9
Odd and even numbers 305.1
Zero as an even number 305.3
Consecutive numbers 305.3
0, 2, 4, 6, 8 as even numbers 305.3
Odd + odd, odd + even, even + even 305.5
Evaluating TRUE and FALSE statements 305.5
Counting up in 3s 305.7
Counting up and down in 3s 305.9
Whole division by 3 306.0
Assignment arrow 306.1
Remainder on division by 3 306.2
Sequence generated by division modulus 3 306.4
Indefinite repetition of modular sequence 306.5
Infinity 306.5
Counting up in 4s 306.6
Counting up and down in 4s 306.8
Whole division by 4 306.9
Remainder on division by 4 307.1
Divison by both 3 and 4 307.3
Both, two conditions together, AND 307.3
Neither, nor, OR 307.5
Counting backwards in 4s 307.7
Negative numbers 308.1
Counting down in 4s with negative numbers 308.1
Counting up and down in 5s 308.3
Rule or test - divisibility by 5 308.5
Criterion (implicit concept of a rule or test) 308.5
Counting up and down in 5s with negative numbers 308.7
Comprehension of two factor number statement 308.9
SUM of two numbers 308.9
Operators 309.1
Addition and multiplication symbols 309.2
Two and multifactor sequence of operations 309.3

RAW CONTENT OF THE WORKOUT

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SLIDE 1 Count up and down the first ten numbers REPEAT ALOUD SLIDE 2 Count ALOUD up and down the first ten numbers. GO BACK TO THE PREVIOUS SLIDE IF YOU NEED TO. SLIDE 3 Count ALOUD up and down in tens up to one hundred REPEAT ALOUD SLIDE 4 Count ALOUD up and down in tens up to one hundred. GO BACK TO THE PREVIOUS SLIDE IF YOU NEED TO. SLIDE 5 Count ALOUD up from 1 to 20, and back down to 0. SLIDE 6 Count ALOUD up from 1 to 20, and back down to 0. Use the previous slide if you need to see the numbers. SLIDE 7 Count aloud in twos up from 2 to 20, and back down to 0. SLIDE 8 Count aloud in twos up from 0 to 20, and back down to 0. Use the previous slide if you need to see the numbers. SLIDE 9 Complete the following sequence up to the number 21. You are adding 2 each time. Count from memory from 1 to 21 and back down to 1. SLIDE 10 SLIDE 11 Complete the following table SLIDE 12 SLIDE 13 ? Is the number 0 an odd number or an even number? ? are CONSECUTIVE numbers. I have twenty consecutive numbers. How many of these are odd? How many of these are even? ? How can we tell whether a number is an EVEN number? SLIDE 14 ? Is the number 0 an odd number or an even number? Answer. Zero is an even number. ? I have twenty consecutive numbers. How many of these are odd? How many of these are even? Answer. Ten are odd, ten are even. Twenty is an even number. In any such list there must be as many even numbers as there are odd numbers. Half of 20 is 10. Reason. The sequence goes ODD, EVEN, ODD, EVEN … ? How can we tell whether a number is an EVEN number? Answer. An even number ends in 0, 2, 4, 6 or 8. There are alternative answers. For example, an even number can be divided by 2. SLIDE 15 ? If I add an ODD number to an EVEN number, is the sum odd or even? ? Someone once said, “If you add an even number to an even number the result is an odd number”. Is this TRUE or FALSE? SLIDE 16 ? If I add an ODD number to an EVEN number, is the sum odd or even? Answer. The sum of an ODD and an EVEN number is ODD. Example. 5 + 2 = 7. 5 is odd, 2 is even, 7 is odd. ? Someone once said, “If you add an even number to an even number the result is an odd number”. Is this TRUE or FALSE? Answer. This statement is FALSE. If you add an even number to an even number, the result is an even number. Example. 4 + 6 = 10. 4 is even, 6 is even, 10 is even. SLIDE 17 Complete the following sequence up to the number 36. You are adding 3 each time. SLIDE 18 SLIDE 19 Count aloud in threes up from 0 to 36, and back down to 0. Use the previous slide if you need to see the numbers. SLIDE 20 How many times does three divide into the following numbers? (a) 27 (b) 18 (c) 21 (d) 33 (e) 15 (f) 24 (g) 36 (h) 12 SLIDE 21 (a) 27 ? 9 (b) 18 ? 6 (c) 21 ? 7 (d) 33 ? 11 (e) 15 ? 5 (f) 24 ? 8 (g) 36 ? 12 (h) 12 ? 4 SLIDE 22 What is the remainder when the following numbers are divided by 3? (a) 50 (b) 13 (c) 42 (d) 31 SLIDE 23 (a) 50 ? 2 (b) 13 ? 1 (c) 42 ? 0 (d) 31 ? 1 SLIDE 24 Complete the following table What does the table show? SLIDE 25 The table shows the remainder when a number is divided by 3. The pattern 0, 1, 2 repeats itself infinitely. SLIDE 26 Complete the following sequence up to the number 48. You are adding 4 each time. SLIDE 27 SLIDE 28 Count aloud in fours up from 0 to 48, and back down to 0. Use the previous slide if you need to see the numbers. SLIDE 29 How many times does four divide into the following numbers? (a) 24 (b) 8 (c) 12 (d) 36 (e) 28 (f) 16 (g) 48 (h) 32 SLIDE 30 (a) 24 ? 4 (b) 8 ? 2 (c) 12 ? 3 (d) 36 ? 9 (e) 28 ? 7 (f) 16 ? 4 (g) 48 ? 8 (h) 12 ? 3 SLIDE 31 What is the remainder when the following numbers are divided by 4? (a) 35 (b) 23 (c) 55 (d) 28 SLIDE 32 (a) 35 ? 3 (b) 23 ? 3 (c) 42 ? 2 (d) 28 ? 0 SLIDE 33 Which of the following numbers can be divided by both 3 and 4? (a) 11 (b) 24 (c) 27 (d) 48 (e) 72 (f) 65 (g) 37 (h) 100 SLIDE 34 (a) 11 ? no (b) 24 ? yes (c) 27 ? yes (d) 48 ? yes (e) 72 ? yes (f) 65 ? no (g) 37 ? no (h) 100 ? no SLIDE 35 Which of the following numbers can be divided by neither 3 nor 4? (a) 13 (b) 16 (c) 22 (d) 36 (e) 41 (f) 27 (g) 44 (h) 52 SLIDE 36 (a) 13 ? yes, neither (b) 16 ? no, divisible by 4 (c) 22 ? yes, neither (d) 36 ? no, divisible by both 3 and 4 (e) 41 ? yes, neither (f) 27 ? no, divisible by 3 (g) 44 ? no, divisible by 4 (h) 52 ? no, divisible by 4 SLIDE 37 Complete the following sequence. You are counting backwards in fours. SLIDE 38 SLIDE 39 Complete the following sequence. You are counting backwards in fours. SLIDE 40 SLIDE 41 Complete the following sequence. You are counting backwards in fours. SLIDE 42 SLIDE 43 Count aloud in fives up from 0 to 60, and back down to 0. SLIDE 44 SLIDE 45 Someone says “113 can be divided by 5”. How can you tell without doing any calculation that this person is wrong? SLIDE 46 Any number that can be divided by 5 ends in a 0 or a 5. 113 ends in a 3, so 113 cannot be divided by 5. SLIDE 47 Count down and then up from 15 to -20 in fives. SLIDE 48 SLIDE 49 The remainder when 18 is divided by 5 is added to the remainder when 23 is divided by 4. What is this sum? SLIDE 50 When 18 is divided by 5, the remainder is 3. When 23 is divided by 4, the remainder is 3. The sum is 6. SLIDE 51 Complete the following ? ? ? SLIDE 52 Complete the following ? Answer 27 ? Answer 26 ? Answer 8 SLIDE 53 The remainder when 47 is divided by 5 is added to the remainder when 22 is divided by 3. Is the sum an even number? SLIDE 54 When 47 is divided by 5 the remainder is 2. When 22 is divided by 3 the remainder is 1. . This is not an even number. Answer: No