Grade 1 · Mathematical Practice · MAT-01-MATHPRACTICE-001
Explain a Solution with Pictures, Numbers, and Words
Represent the same mathematical idea with a picture, numbers, and words.
Learning objectives
What you should be able to do
- Represent the same mathematical idea with a picture, numbers, and words.
- Explain how each representation connects to the others.
- Use mathematical vocabulary to communicate a solution clearly.
Prerequisite check
Make sure the foundation is ready.
Provides a familiar mathematical situation to represent in multiple ways.
Learn
Build the idea from meaning, not memorization.
A strong solution shows thinking, not just an answer
A correct number is useful, but mathematics also asks how we know. Pictures can show quantities, equations can record relationships, and words can explain the reasoning that connects them.
Different representations reveal different information
A drawing can make a story concrete, an equation can make the structure compact, and a sentence can explain what each number means. Using more than one representation helps catch mistakes and deepens understanding.
Representations should agree
If a picture shows 7 objects but the equation says 5 + 1 = 6, the representations do not match. Checking agreement among pictures, numbers, and words is a powerful self-check.
Explain the meaning of the numbers
Good mathematical communication does more than read an equation aloud. It identifies what the numbers stand for in the problem and why the chosen operation fits the situation.
Interactive math lab
Change it. See what stays true.
Equation Balance
Adjust both sides. Equality means both expressions have the same value.
Balanced: both sides have equal value.
- story to picture
- picture to equation
- equation to words
- find representation mismatch
Worked examples
Twenty different ways to see the concept work.
Story: 3 apples and 2 more apples arrive.
Picture: 3 dots + 2 dots; Equation: 3+2=5; Words: Five apples altogether.All three forms describe the same joining situation.
Story: 7 birds, 2 fly away.
Picture: 7 marks with 2 crossed out; Equation: 7−2=5; Words: Five birds remain.The drawing and subtraction equation match the action.
Show 8 as tens and ones.
Picture: 8 ones; Number: 8; Words: eight ones.Representations identify the same quantity.
Show 14 as tens and ones.
Picture: one ten-stick and four ones; Number: 14; Words: one ten and four ones.Place-value picture, numeral, and words agree.
Compare 12 and 15.
Picture: base-ten models; Number: 12<15; Words: 15 has three more ones after equal tens.The explanation identifies why 15 is greater.
Show 10 more than 23.
Number line jump +10; Equation: 23+10=33; Words: one more ten changes 23 to 33.Multiple forms show the same place-value change.
Measure a pencil with 6 cubes.
Picture: 6 cubes end-to-end; Number: 6 cubes; Words: the pencil is six cube-lengths long.Units and count are connected.
Tell time at 4:00.
Clock picture; Number: 4:00; Words: four o'clock.Three representations identify the same time.
A graph shows 5 cats and 3 dogs.
Picture graph; Number: 5−3=2; Words: there are two more cats than dogs.The equation describes the graph comparison.
A square divided into two equal parts.
Picture: two equal regions; Number idea: 2 equal shares; Words: each region is one half.The picture and language define halves.
What is wrong if a picture has 6 objects but equation says 4+1=5?
Representations disagreeOne or both representations must be corrected.
Story says 'altogether' but equation subtracts.
Likely operation mismatchJoining language usually indicates addition in this context.
Equation 9−4=5; explain 9.
9 is the starting amountGood explanations assign meaning to numbers.
Equation 9−4=5; explain 4.
4 is the amount removedEach number has a role.
Equation 9−4=5; explain 5.
5 is what remainsThe result connects back to the story.
Picture shows two groups of 4 and 3.
Equation: 4+3=7The equation records the join shown visually.
Words say 'seven is two more than five.'
Equation: 7=5+2Words can be translated to numbers.
Equation says 6=10−4.
Story: 10 objects, 4 removed, 6 remainNumbers can be translated back into a situation.
Why use labels in drawings?
They clarify what objects and numbers representLabels make communication precise.
Why explain when answer is already correct?
Explanation shows reasoning and can reveal hidden misunderstandingsMathematics values justified thinking.
Practice
Guided practice with hints
01Show 4+3=7 with a picture and a sentence.
Hint: Draw 4 objects, then 3 more.
Answer: Any matching 7-object drawing plus a sentence explaining the join.
02Explain what 8 means in 8−2=6 for a take-away story.
Hint: It is the amount before anything is removed.
Answer: The starting amount.
03A picture shows 5 objects and 2 crossed out. Write an equation.
Hint: Start with 5 and subtract the 2 removed.
Answer: 5−2=3
04If your drawing and equation disagree, what should you do?
Hint: Use one representation to check the other.
Answer: Recheck and correct the mismatch.
05Represent 13 using tens and ones plus words.
Hint: Think one ten and three ones.
Answer: 1 ten + 3 ones; thirteen.
06Why might a picture help with a word problem?
Hint: It makes quantities and actions visible.
Answer: It helps show what is happening and how quantities relate.
Practice
Independent practice
01Represent 2+5=7 with a picture.
Answer: Any correct picture showing 2 and 5 combining to 7.
02Explain the 3 in 7−3=4.
Answer: It is the amount taken away.
03Write words for 6+1=7.
Answer: Six plus one makes seven / one more than six is seven.
04Show 12 with tens and ones.
Answer: 1 ten and 2 ones.
05What should happen if picture and equation disagree?
Answer: Recheck and correct them.
06Why label a math drawing?
Answer: To show what the objects and numbers mean.
07Translate 'five more than three is eight' into an equation.
Answer: 3+5=8
08Translate 10−2=8 into a simple story.
Answer: Any valid story starting with 10, removing 2, leaving 8.
Common mistakes
Learn to catch the error, not just the answer.
Trace each number in the equation back to a visible quantity or action.
Add at least one sentence explaining what the numbers mean and why the operation fits.
Use drawings to represent quantities, groups, changes, or relationships directly.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Explain a homework solution to someone using one drawing, one equation, and one sentence.
- Use multiple representations to check a shopping or counting situation at home.
Challenge problems
Create two different pictures that both represent 5+3=8.
Any two mathematically equivalent drawings.
Can two different equations match the same picture? Give an example.
Yes; a 3-and-2 part-whole picture can match 3+2=5 and 5−2=3.
Why can a clear explanation reveal a mistake even when the final answer looks plausible?
The reasoning may show that numbers or operations were used with the wrong meaning.
Explain 14<17 using a picture, numbers, and words.
Any consistent base-ten comparison showing equal tens and 4<7 ones.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Match the Math
Match stories, pictures, equations, and explanations that represent the same situation.
Practice
Mastery check
01Name three ways to represent a solution.
Answer: Pictures, numbers/equations, and words.
02Why should the representations agree?
Answer: They describe the same mathematical situation.
03If a drawing shows 6 but equation totals 5, what should you do?
Answer: Recheck and correct the mismatch.
04Explain the starting number in 9−3=6.
Answer: 9 is the amount before 3 is removed.
05Show 15 as tens and ones in words.
Answer: One ten and five ones.
06Why is a correct answer alone sometimes not enough?
Answer: It does not show how the reasoning works.
07Translate a simple picture of 2 objects plus 4 objects into an equation.
Answer: 2+4=6
08Translate 7−2=5 into a sentence.
Answer: Seven take away two leaves five.
Terminology
Words to know
- representation
- A way to show a mathematical idea, such as a picture, equation, model, or words.
- equation
- A statement showing two mathematical expressions are equal.
- justify
- Explain why a mathematical answer or method makes sense.
- label
- A word or symbol identifying what part of a representation means.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematical Practice — MP1, MP2, MP3, MP4
Reasoning, representation, modeling, and communication practices.