🔢 MathGrade 2Lesson 7
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Complete Number Sequences

Lesson preview: the Mini Lesson and Vocabulary are open to everyone. Guided practice, exercises, the parent checklist and the printable PDF worksheet come with full access (free 7-day trial or membership).

What you will learn

  • 1Find the rule in a counting sequence
  • 2Fill in two or more consecutive missing numbers when counting forward or backward
  • 3Verify each completed sequence by checking every step is the same size
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Mini Lesson

In Lesson 5 you found one missing number. Now we will complete whole stretches of a sequence — two, three, or more gaps in a row. The strategy is the same, but we apply it step by step.

Step-by-step strategy

  • Step 1 — Find the rule. If two given numbers are next to each other, subtract the smaller from the larger. If there are blanks between them, find the difference and split it into equal steps.
  • Step 2 — Write the rule above the sequence. This keeps you from forgetting it midway.
  • Step 3 — Fill each blank one at a time. Add the rule to (or subtract it from) the last number you wrote.
  • Step 4 — Check. Scan the completed sequence: is each step exactly the same size?

Example — counting forward

  • Sequence: 415, ___, ___, 445, ___
  • Rule: 445 − 415 = 30. There are 3 equal steps, and 10 + 10 + 10 = 30 → +10 per step. Check: 415, 425, 435, 445 — then +10 → 455.

Example — counting backward

  • Sequence: 560, ___, ___, 530
  • Rule: 560 − 530 = 30. There are 3 equal steps, and 10 + 10 + 10 = 30 → −10 per step: 560, 550, 540, 530.

Words to know

Sequence

An ordered list of numbers that follow a rule

e.g. 415, 425, 435, 445 is a sequence.

Rule

The amount you add or subtract between numbers in a sequence

e.g. The rule of this sequence is plus 10.

Gap

A blank spot in a sequence where a number is missing

e.g. There is a gap between 415 and 445 to fill in.

Forward

Counting from smaller to larger numbers

e.g. We counted forward by tens: 415, 425, 435.

Backward

Counting from larger to smaller numbers

e.g. 560, 550, 540 counts backward by tens.

Step

Each jump from one number to the next in a sequence

e.g. Each step in this sequence is +10.

Completing a forward sequence: 415 to 455 by 10sA number line showing 415, then two blank boxes, then 445, then a blank box. The rule plus 10 is shown between each step. Filled sequence: 415, 425, 435, 445, 455.Complete the Sequence (+10)Rule: +10415+10→425+10→435+10→445Now extend one more step:445+10→455Step 4 — Check each jump is +10
Step-by-step completion of 415, ___, ___, 445, ___ with rule +10, giving 425, 435, then 455.
Completing a backward sequence: 560 to 530 by 10sSequence: 560, blank, blank, 530. Total difference: 30, which is 3 equal steps of 10. Rule minus 10. Filled: 560, 550, 540, 530.Backward Sequence (−10)Find the rule:560 − 530 = 30; 10 + 10 + 10 = 30 → rule: −10Rule: −10560−10→550−10→540−10→530560, 550, 540, 530
The backward sequence 560, ___, ___, 530 solved by finding the total difference (30 is 3 equal steps of 10), giving rule −10 and answers 550, 540.
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Ask yourself: "How many steps are between my known numbers? What step size, added that many times, makes the total difference?"

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← Lesson 6: Identify Odd and Even NumbersLesson 8: Solve Place Value Riddles →