A student needs to solve 2 + 7. Which strategy gets to the answer fastest?
ACount all objects from 1 to 9
BStart at 2 and count on 7 more: 2... 3, 4, 5, 6, 7, 8, 9
CStart at 7 and count on 2 more: 7... 8, 9
DMemorize the answer without any counting strategy
Counting on from the LARGER number is the most efficient strategy. Starting at 7 and counting on just 2 steps (8, 9) reaches the answer much faster than starting at 2 and counting on 7 steps, or counting all 9 objects from scratch. The strategy works because addition is commutative — the order of the addends doesn't change the sum.
Question 2 Multiple Choice
What is 8 + 0?
A0 — adding zero gives you zero
B1 — zero counts as the next number
C9 — zero comes right after 8
D8 — adding zero leaves the number unchanged
Adding zero means joining a group of 8 things with NO additional things, so the total stays 8. The misconception in option A confuses adding zero with multiplying by zero or replacing a number. Option C confuses adding zero with counting forward one step. The rule 0 + n = n (and n + 0 = n) is one of the most important basic facts to recognize automatically.
Question 3 True / False
To solve 3 + 6, it is more efficient to start from 6 and count on 3 more than to count all the way from 1 to 9.
TTrue
FFalse
Answer: True
Counting on from the larger number (start at 6, say '7, 8, 9' — only 3 steps) is faster than counting all (start at 1 and count 9 steps to reach the total). This strategy becomes even more valuable with larger numbers. Students who always count from 1 take much longer and make more errors than those who count on from the bigger addend.
Question 4 True / False
4 + 0 = 0, because adding zero means there is very little to add.
TTrue
FFalse
Answer: False
4 + 0 = 4, not 0. Adding zero means joining your group of 4 things with an empty group — nothing new comes in, so the total stays 4. The misconception 'zero means nothing, so the answer is zero' confuses the value of zero (nothing extra) with making the whole answer disappear. Zero is a quantity — it just means none — and adding none to something leaves that something unchanged.
Question 5 Short Answer
Why is it faster to count on from the larger number than to count all objects from the beginning?
Think about your answer, then reveal below.
Model answer: When you count on from the larger number, you skip the steps you've already 'counted' inside that number. For 3 + 6, starting at 6 means you only need 3 more counting steps (7, 8, 9), instead of restarting from 1 and counting all 9 objects.
This strategy works because the larger number already represents a counted group — you don't need to recount what's already there. Counting all is reliable but slow; counting on treats the larger addend as a known starting point and only adds the smaller amount incrementally. As facts become memorized, even counting on disappears — but understanding why it works is the conceptual foundation for fact fluency.