A child looks at 8 + 4 = 10 + 2 and says it is wrong because an answer should come after the equal sign. The calculation is within reach, but the child is reading the symbol as a command: “work this out.”
Knowing how to teach the equal sign starts with uncovering that interpretation. Instead of repeating a definition, you can ask questions and use equations that show whether children understand that both sides have the same value. Teaching Story Writing with Four-Picture Sequences
You will be able to identify command-style thinking, teach the language “the same as,” and use nonstandard equations to check understanding. You will also have number comparison activities and clear signs for deciding when to introduce further comparison symbols. Teach Keyboarding With Shared Devices
Contents
Listen for command-style interpretations first
Begin with a short conversation rather than another explanation. Show a child 7 + 5 = 12 and ask, “What does the equal sign tell you?” Follow this with 12 = 7 + 5 and 7 + 5 = 10 + 2.
Listen to the words the child chooses and whether changing the equation’s arrangement changes the answer. An article in Learning Disabilities Research & Practice describes how students can react to the equal sign as a command to do something or write an answer, rather than considering its relational meaning.
- “It means the answer is next.” This suggests a command-style interpretation.
- “It means makes.” Ask what “makes” means here; the word alone does not reveal the child’s thinking.
- “Both sides are twelve.” Ask how the child knows. A clear comparison is stronger evidence than a correct answer alone.
- “The second one is backwards.” This suggests that equation layout, rather than equality, is guiding the decision.
Do not correct every response immediately. Ask, “Could the equal sign still mean the same thing if I turn the equation around?” or “What amount is on each side?” Record the child’s words so you can compare them with later explanations.
One incorrect answer does not establish a fixed misconception. Check several arrangements and include equations the child can calculate easily, so difficult arithmetic does not hide their interpretation of the symbol.
Teach “the same as” in number sentences
Teach children to read the equal sign as “the same as.” For 6 + 2 = 5 + 3, model the full sentence: “Six plus two has the same value as five plus three.” Then ask the child to say it without shortening the equal sign to “the answer is.”
The phrase needs a visible meaning. Build six plus two with counters on one mat and five plus three on another. Confirm that each mat contains eight counters, then place the equal sign card between the two collections.
Explain that each side can look different while representing the same amount. An expression, such as 6 + 2, names a quantity. An equation, such as 6 + 2 = 5 + 3, states that the expressions on its two sides have equal value.
A practice-focused Intervention in School and Clinic article reports that, across several studies involving students with mathematics difficulty, those receiving explicit instruction in the relational definition “the same as” demonstrated improved performance on equation tasks. Keep your instruction explicit by connecting the phrase, symbol, quantities and spoken explanation each time.
Vary the examples while preserving the language. Use 9 = 9, 4 + 5 = 9, 9 = 4 + 5 and 4 + 5 = 6 + 3. Ask, “What is the same as what?” rather than “What is the answer?”
You can still teach calculation. Simply separate the two questions: “What is the value of this expression?” and “Does it have the same value as the expression on the other side?”
Use nonstandard equations to reveal their thinking
Use nonstandard equations as a quick check of what the child believes. These equations place an expression or missing number somewhere other than the familiar answer position. Examples include 10 = 6 + 4 and 3 + 4 = __ + 5.
The second example is especially revealing. A child who writes seven may have calculated the left side and treated the blank as the answer position. A child who writes two and explains that both sides must equal seven is comparing the two quantities.
This type of task is supported directly by the evidence ledger. The Learning Disabilities Research & Practice article identifies nonstandard equations as one way to assess equal-sign understanding because responses can provide clues about operational and relational interpretations.
Start with familiar numbers so the equation structure remains the focus. Show 8 = 5 + 3, then 4 + 3 = 6 + 1, followed by 8 + 5 = __ + 6. Ask the child to decide what belongs in the blank and explain how both sides are related.
Include true-or-false prompts such as 5 + 4 = 6 + 3 and 7 + 2 = 7 + 3. A child should not decide that both are correct merely because each side contains an addition sign. Ask for a correction when an equation is false.
Change one feature at a time. If you introduce unfamiliar operations, large numbers and an unusual blank position together, an incorrect response will tell you little about the specific barrier.
Ask children to compare both sides before they calculate
Establish a routine in which children examine both sides before calculating. Point to the left expression, the equal sign and the right expression in turn. Ask children to name each quantity and predict whether the values could be the same.
- Read: Say the complete number sentence, using “is the same as” for the equal sign.
- Represent: Build, draw or mark each quantity on separate sides of a line.
- Compare: Look for useful relationships before calculating each side.
- Check: Calculate when needed and decide whether the equation is true.
- Explain: Describe why the two sides do or do not have the same value.
For 9 + 6 = 10 + 5, a child might notice that one has moved from nine to ten while six has decreased to five. That observation compares the expressions directly. The child can then calculate both sides as a check.
Use number comparison activities that do not always include a blank. Give pairs of expression cards, such as 7 + 4 and 8 + 3, and ask children to find pairs with the same value. You can also ask them to build two matching collections with counters, then write an equation describing them.
Another useful activity is “make it true.” Display 6 + 5 = 6 + 4 and allow a child to change one number, operation or side. Require an explanation of how the change makes the values match.
During whole-class responses, ask for reasoning before accepting a chorus of “true” or “false.” A sentence such as “both sides equal eleven” gives you more information than the correct verdict alone.
Decide when children are ready for further comparison symbols
Use children’s explanations to decide what to revisit next. Check whether they can explain that the equal sign means “the same as” in familiar and nonstandard equations. The Learning Disabilities Research & Practice article identifies nonstandard equations as a way to assess whether a child is interpreting the sign operationally or relationally.
- They read 14 = 9 + 5 without calling it backwards.
- They complete 7 + 6 = __ + 5 and explain how the values match.
- They decide whether 8 + 3 = 7 + 5 is true and justify the decision.
- They use “the same value as” consistently, even when there is no blank.
- They can represent the two sides with objects, drawings or quantities on a number line.
These checks focus on meaning rather than symbol recall. Nonstandard equations can provide evidence about whether children are using an operational or relational interpretation, as described in Learning Disabilities Research & Practice. Explicit teaching of “the same as” is also the approach discussed in the Intervention in School and Clinic article.
If children still search automatically for an answer after the equal sign, continue with matching, true-or-false and missing-number equations. You can compare quantities orally with “more than,” “less than” and “the same as” without rushing to add all three symbols.
When children explain equality reliably, introduce the new comparison symbols as labels for different relationships. Keep mixing equality examples into the practice so that = remains an active comparison choice rather than the symbol used whenever two numbers appear.
The goal is an explanation you can hear and see in action: the equal sign means that two quantities have the same value. Children should be able to apply that meaning whether the answer space appears at the end, the beginning or within an equation.
Keep the routine simple. Ask children to read both sides, represent each amount and explain the relationship. Their responses will show you whether to continue with equality work or introduce further comparison symbols.
