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Copy and complete the following number patterns: 1.1. -3; -2; -1; _; ; ; 1.2. -10; -9; -8; ; ; ; 1.3. 8; 10; ; ; ; ; _ 2. Show each of the above number rows on a separate number line.

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2 parts
2.1

−10;0;2;5;7\mathbf{-10; 0; 2; 5; 7}

−34;−15;1;8;12\mathbf{-34; -15; 1; 8; 12}

−567;−1;0;54;112\mathbf{-567; -1; 0; 54; 112}

2.2

6;4;0;−6;−15\mathbf{6; 4; 0; -6; -15}

16;12;2;−1;−23\mathbf{16; 12; 2; -1; -23}

124;1;−1;−84;−147\mathbf{124; 1; -1; -84; -147}

Step-by-step solution

7 steps

Here are the solutions to the questions from your worksheet.

Part 1

Number Patterns

Part 1.1· 7 steps

Copy and complete the following number patterns

  • 1.1.1. −5;−2;−1;_;_;_;5-5; -2; -1; \_ ; \_ ; \_ ; 5 The pattern of differences is +3,+1,+1,+1,+1,+3+3, +1, +1, +1, +1, +3.

  1. Find the differences between the given numbers.

    $-2 - (-5) = 3$  
$-1 - (-2) = 1$

  2. Assume a symmetrical pattern of differences to fit the remaining numbers and the final 5.

    The sequence of differences is $3, 1, 1, 1, 1, 3$.

  3. Complete the pattern.

    $-1 + 1 = 0$  
$0 + 1 = 1$  
$1 + 1 = 2$  
$2 + 3 = 5$ (This matches the last given number)  
The completed pattern is: $-5; -2; -1; \mathbf{0}; \mathbf{1}; \mathbf{2}; 5$
    • 1.1.2. −10;−9;−8;_;_;_;4;_;_-10; -9; -8; \_ ; \_ ; \_ ; 4; \_ ; \_ This pattern consists of two segments, each increasing by 1.

  4. Complete the first segment by adding 1 to each term.

    $-8 + 1 = -7$  
$-7 + 1 = -6$  
$-6 + 1 = -5$

  5. Complete the second segment by adding 1 to each term, starting from 4.

    $4 + 1 = 5$  
$5 + 1 = 6$  
The completed pattern is: $-10; -9; -8; \mathbf{-7}; \mathbf{-6}; \mathbf{-5}; 4; \mathbf{5}; \mathbf{6}$
    • 1.1.3. 8;10;_;16;_8; 10; \_ ; 16; \_ This is an arithmetic progression with a common difference of 2.

  6. Find the common difference.

    $10 - 8 = 2$

  7. Complete the pattern by adding 2 to each term.

    $10 + 2 = 12$  
$12 + 2 = 14$ (This is the number before 16, so it fits)  
$16 + 2 = 18$  
The completed pattern is: $8; 10; \mathbf{12}; 16; \mathbf{18}$

Part 1.2

Show each of the above number rows on a separate number line.

  • 1.1.1. Number Line:

    ⟷∙−5∘−4∘−3∙−2∙−1∙0∙1∙2∘3∘4∙5⟶\longleftrightarrow \quad \underset{-5}{\bullet} \quad \underset{-4}{\circ} \quad \underset{-3}{\circ} \quad \underset{-2}{\bullet} \quad \underset{-1}{\bullet} \quad \underset{0}{\bullet} \quad \underset{1}{\bullet} \quad \underset{2}{\bullet} \quad \underset{3}{\circ} \quad \underset{4}{\circ} \quad \underset{5}{\bullet} \quad \longrightarrow

  • 1.1.2. Number Line:

    ⟷∙−10∙−9∙−8∙−7∙−6∙−5∘−4∘−3∘−2∘−1∘0∘1∘2∘3∙4∙5∙6⟶\longleftrightarrow \quad \underset{-10}{\bullet} \quad \underset{-9}{\bullet} \quad \underset{-8}{\bullet} \quad \underset{-7}{\bullet} \quad \underset{-6}{\bullet} \quad \underset{-5}{\bullet} \quad \underset{-4}{\circ} \quad \underset{-3}{\circ} \quad \underset{-2}{\circ} \quad \underset{-1}{\circ} \quad \underset{0}{\circ} \quad \underset{1}{\circ} \quad \underset{2}{\circ} \quad \underset{3}{\circ} \quad \underset{4}{\bullet} \quad \underset{5}{\bullet} \quad \underset{6}{\bullet} \quad \longrightarrow

  • 1.1.3. Number Line:

    ⟷∙8∘9∙10∘11∙12∘13∘14∘15∙16∘17∙18⟶\longleftrightarrow \quad \underset{8}{\bullet} \quad \underset{9}{\circ} \quad \underset{10}{\bullet} \quad \underset{11}{\circ} \quad \underset{12}{\bullet} \quad \underset{13}{\circ} \quad \underset{14}{\circ} \quad \underset{15}{\circ} \quad \underset{16}{\bullet} \quad \underset{17}{\circ} \quad \underset{18}{\bullet} \quad \longrightarrow

Part 2

Ordering and Comparing Numbers

Part 2.1

−10;0;2;5;7\mathbf{-10; 0; 2; 5; 7}

Write the following numbers in ascending order

  • 2.1.1. 7;−10;5;0;27; -10; 5; 0; 2 The numbers in ascending order are: −10;0;2;5;7\boxed{\mathbf{-10; 0; 2; 5; 7}}

  • 2.1.2. −34;12;1;−15;8-34; 12; 1; -15; 8 The numbers in ascending order are: −34;−15;1;8;12\boxed{\mathbf{-34; -15; 1; 8; 12}}

  • 2.1.3. −567;54;0;112;−1-567; 54; 0; 112; -1 The numbers in ascending order are: −567;−1;0;54;112\boxed{\mathbf{-567; -1; 0; 54; 112}}

Part 2.2

6;4;0;−6;−15\mathbf{6; 4; 0; -6; -15}

Write the following numbers in descending order

  • 2.2.1. 6;−15;4;−6;06; -15; 4; -6; 0 The numbers in descending order are: 6;4;0;−6;−15\boxed{\mathbf{6; 4; 0; -6; -15}}

  • 2.2.2. −23;16;2;−1;12-23; 16; 2; -1; 12 The numbers in descending order are: 16;12;2;−1;−23\boxed{\mathbf{16; 12; 2; -1; -23}}

  • 2.2.3. −147;124;1;−84;−1-147; 124; 1; -84; -1 The numbers in descending order are: 124;1;−1;−84;−147\boxed{\mathbf{124; 1; -1; -84; -147}}

Part 2.3

Copy the following numbers and indicate which one is larger, smaller or equal by using ONE of the following symbols: (<;>;=)(<; >; =)

  • 2.3.1. 24_1224 \_ 12

    24>1224 \mathbf{>} 12

  • 2.3.2. 1_−21 \_ -2

    1>−21 \mathbf{>} -2

  • 2.3.3. +34_34+34 \_ 34

    +34=34+34 \mathbf{=} 34

  • 2.3.4. −324_−342-324 \_ -342

    −324>−342-324 \mathbf{>} -342

  • 2.3.5. 0_−120 \_ -12

    0>−120 \mathbf{>} -12

Part 3

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