Equal sums
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Equal sums: skill guide
| Objective | An equation says that the expression on the left of the equals sign has the same value as the expression on the right. |
|---|---|
| Grade | Grade 1 |
| Standard | CCSS.MATH.CONTENT.1.OA.D.7 |
| Difficulty | Developing · Abstract |
| Representation | Numerical equation |
| Practice format | Interactive, account-free practice with immediate feedback |
Objective
An equation says that the expression on the left of the equals sign has the same value as the expression on the right.
What this practice covers
An equation says that the expression on the left of the equals sign has the same value as the expression on the right. In this practice, both sides contain addition and one addend is missing. Learners first find the total of the complete side, then determine what the incomplete side needs to reach that same total. Blanks appear in different positions so the equals sign is understood as a balance, not as a signal that an answer always comes next.
Standards alignment
Supports Common Core: CCSS.MATH.CONTENT.1.OA.D.7 — Understand the meaning of the equal sign and determine whether addition and subtraction equations are true or false.
Who it’s for
This activity is designed for Grade 1 learners who can add within 10 and are ready to reason about equations in more flexible forms. It is especially helpful for children who solve familiar equations such as 3 + 4 = 7 but hesitate when the total or an addition expression appears on the left side of the equals sign.
What to know first
- Learners should understand addition as combining two parts and should be able to find sums through 10 with objects, drawings, counting on, or recalled facts. They should recognize the symbols + and =. Automatic fact recall is helpful but not required.
Difficulty and scaffolding
Developing · Abstract stage
Problem representations
- Numerical equation
Three worked examples
- For 5 + 1 = 4 + ?, the complete side totals 6. Four needs 2 more to make 6, so the missing number is 2.
- For ? + 5 = 2 + 6, the right side totals 8. Five needs 3 more to make 8, so the missing number is 3.
- For 3 + 7 = ? + 4, the left side totals 10. The other side needs 6 because 6 + 4 = 10.
Likely misconceptions
- A common mistake is to add all visible numbers together or assume the equals sign means ‘the answer comes next.’ Learners may also solve the incomplete side without first checking the complete side’s total. Encourage a two-step habit: find the value of the side with no blank, then make the other side match it. Finally, add both sides to check.
Hints and explanations
- For 5 + 1 = 4 + ?, the complete side totals 6. Four needs 2 more to make 6, so the missing number is 2.
- For ? + 5 = 2 + 6, the right side totals 8. Five needs 3 more to make 8, so the missing number is 3.
- For 3 + 7 = ? + 4, the left side totals 10. The other side needs 6 because 6 + 4 = 10.
What to practice next
After equal sums within 10 feel secure, practice true-or-false equations and equations with a missing number but no blank box. Learners can then extend the same balancing idea to subtraction, addition within 20, and early relational thinking such as deciding which side is greater or less.
Editorial review
Reviewed by Brilliant’s curriculum team. Exercises are generated within defined difficulty ranges and checked against verified answer rules.
Equal sums FAQs
What does the equals sign mean?
The equals sign means ‘has the same value as.’ It tells us that the amount on one side is equal to the amount on the other side. It does not mean that an answer must appear immediately after it, so equations can be written in several valid forms.
What is the best way to solve an equal-sums problem?
Start with the side that has no blank and find its total. Then look at the known number beside the blank and ask what must be added to reach that same total. Check by adding both sides separately and confirming that the results match.
Why does the blank move to different positions?
Changing the blank’s position prevents learners from relying on a single visual pattern. It helps them attend to the relationships among the numbers and understand that addition can appear on either side of the equals sign while the equation remains balanced.
Should learners use counters or drawings?
Yes, especially when the balancing idea is new. Build the complete side with counters, then build the known part on the other side and add counters until the groups match. Gradually move toward mental strategies as the relationship becomes clear.
How many equal-sums problems should a learner do?
A calm set of 10–15 problems is usually enough for focused practice. Stop earlier if the learner begins guessing or loses track of the two sides. A short explanation of how each side balances is often more valuable than completing a larger number quickly.