🔢 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).
Learning Objectives
- 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. Pick two numbers that are given and are next to each other. Subtract the smaller from the larger to get the rule.
- Step 2 — Write the rule above the sequence. This keeps you from forgetting it mid-way.
- Step 3 — Fill each blank one at a time. Add (or subtract) the rule to 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, divided by 3 gaps → +10 per step. Check: 415, 425, 435, 445 — then +10 → 455.
Example — counting backward
- Sequence: 560, ___, ___, 530
- Rule: 560 − 530 = 30, divided by 3 gaps → −10 per step: 560, 550, 540, 530.
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Ask yourself: "How many gaps are between my known numbers? Divide the total difference by the number of gaps to find the step size."
Vocabulary
Sequence
An ordered list of numbers that follow a rulee.g. 415, 425, 435, 445 is a sequence.
Rule
The amount you add or subtract between numbers in a sequencee.g. The rule of this sequence is plus 10.
Gap
A blank spot in a sequence where a number is missinge.g. There is a gap between 415 and 445 to fill in.
Forward
Counting from smaller to larger numberse.g. We counted forward by tens: 415, 425, 435.
Backward
Counting from larger to smaller numberse.g. 560, 550, 540 counts backward by tens.
Step
Each jump from one number to the next in a sequencee.g. Each step in this sequence is +10.
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