Grade 5 · Predict an additive number pattern · 659 of 750
Predict an additive number pattern: starting term: 8; amount added each step: 8; number of terms: 10
A planning table for a classroom activity begins at 8, adds 8 each time, and lists 10 terms. Find the last term in the stated original list, explain the calculation, and check a related question.
Try the question, use a hint when you need one, and compare your reasoning with the worked solution. The animation starts with this chapter’s values; changing its controls explores a new case.
01 · Make a prediction
Your practice question
A planning table for a classroom activity begins at 8, adds 8 each time, and lists 10 terms. First find the last term in the stated original list. Then answer: What is the next term after the displayed 10 terms?
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A starting point
An additive pattern has a constant difference between neighboring terms. The first term already exists, so reaching term n requires n minus one additions, not n additions.
Work through the reasoning
Step 1
Identify the quantities and the task
A planning table for a classroom activity begins at 8, adds 8 each time, and lists 10 terms. The first task is to find the last term in the stated original list. An additive pattern has a constant difference between neighboring terms. The first term already exists, so reaching term n requires n minus one additions, not n additions.
Step 2
Calculate the original result
Term n = 8 + (n − 1) × 8. Term 10 is 80, after 9 increments of 8. A different starting value shifts every term by the same amount.
Step 3
Complete the follow-up calculation
What is the next term after the displayed 10 terms? 88. Add 8 once more to 80.
The answer
Term n = 8 + (n − 1) × 8. Term 10 is 80, after 9 increments of 8. A different starting value shifts every term by the same amount. Follow-up: 88. Add 8 once more to 80.
Compare the method as well as the result. A different valid method may reach the same answer. Keep exact values until the last step when the question asks for rounding.
02 · Explore the model
See the mathematical relationship move.
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Watch the relationship
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The mathematical idea
A planning table for a classroom activity begins at 8, adds 8 each time, and lists 10 terms. An additive pattern has a constant difference between neighboring terms. The first term already exists, so reaching term n requires n minus one additions, not n additions. Term 10 is 80, after 9 increments of 8. A different starting value shifts every term by the same amount.
Term n = 8 + (n − 1) × 8
03 · Reflect and transfer
Explain what changes and why.
Reveal the terms from left to right. Compare consecutive differences before predicting the final term from the rule. Explain which quantity changes and which relationship stays valid. Use the starting values again before checking your written answer.
This is a distinct guided scenario using a reusable mathematical model. Similar-looking diagrams can represent different given values and conclusions; they are not different mathematical theories.