Addition and Subtraction Practice Quiz with a Step-by-Step Interactive Lesson
Use the quiz at the top of the page to practice addition and subtraction. This is ideal for building number sense, mastering addition and subtraction facts, and improving mental math speed and accuracy. If you want a refresher, click Start lesson to open a step-by-step guide with examples, strategies, and quick checks.
How this addition and subtraction practice works
1. Take the quiz: answer the questions at the top of the page.
2. Open the lesson (optional): review methods for addition and subtraction with models, examples, and quick checks.
3. Retry: return to the quiz and apply what you reviewed right away.
What you will learn in the addition and subtraction lesson
Meaning & vocabulary
Addition as combining and counting on
Subtraction as take away and difference
Addends, sum, minuend, subtrahend, difference
Models & relationships
Number line hops (forward for addition, backward for subtraction)
Make a ten and bridge through tens (e.g. \(9+6=10+5\))
Doubles and near doubles (e.g. \(7+7\), \(7+8\))
Compensation (adjust and fix) for fast subtraction (e.g. \(52-19=52-20+1\))
Accurate counting on/back for tricky facts
Bigger numbers & word problems
Place value: ones, tens, hundreds
Regrouping (carrying and borrowing) for multi-digit addition and subtraction
Multi-step expressions like \(10+4-2\) and \(25+15-30\)
Word problems with totals, change, distance, and comparing quantities
Back to the quiz
When you are ready, return to the quiz at the top of the page and continue practicing addition and subtraction.
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Addition & Subtraction Lesson
Step-by-step guide
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Addition & Subtraction Lesson
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Lesson Overview
Lesson overview
Purpose: Build a clear understanding of addition and subtraction, learn reliable strategies, and practice checking your work.
Success criteria
Explain \(a+b\) as combining or counting on.
Explain \(a-b\) as take away or finding the difference.
Use key vocabulary: addend, sum, minuend, subtrahend, difference.
Use models like a number line, ten frames, and part-part-whole diagrams.
Add and subtract multi-digit numbers using place value and regrouping (carrying/borrowing).
Solve multi-step expressions such as \(10+4-2\) by working left to right (after parentheses).
Check answers using inverse operations (addition ↔ subtraction).
Key vocabulary
Addend: a number being added (in \(a+b\), both \(a\) and \(b\) are addends).
Sum: the result of addition (the sum of \(a+b\)).
Minuend: the starting number in subtraction (in \(a-b\), \(a\) is the minuend).
Subtrahend: the number you subtract (in \(a-b\), \(b\) is the subtrahend).
Difference: the result of subtraction (the difference of \(a-b\)).
Quick pre-check
Pre-check 1: Which expression shows "add 3 and 4"?
Hint: The plus sign \(+\) means add (combine).
Pre-check 2: Compute \(9+6\).
Hint: Make a ten: \(9+6 = (9+1)+5 = 10+5\).
Addition
Addition: combine and count on
Learning goal: Understand what \(a+b\) means, use a number line idea, and compute sums accurately.
Key idea
Addition means putting parts together to make a total. When you see \(a+b\), you can think: start at \(a\) and add \(b\) more. On a number line, addition is like hopping forward.
Important property
Addition is commutative, which means you can switch the order and the sum stays the same: \(\,a+b=b+a\).
Worked example
Example: \(8+7\)
Make a ten: \(8+7 = (8+2)+5\). \(8+2=10\), then \(10+5=15\). So, \(8+7=15\).
Try it
Try it 1: Compute \(6+8\).
Hint: \(6+8\) can be \(6+4+4 = 10+4\).
Try it 2: Which statement is the commutative property of addition?
Hint: "Commutative" means you can switch the order.
Summary
\(a+b\) means combine parts to make a total (or count on).
You can switch addends: \(a+b=b+a\).
Subtraction
Subtraction: take away and find the difference
Learning goal: Understand what \(a-b\) means and connect subtraction to addition (inverse operations).
Key idea
Subtraction can mean take away (remove from a set) or difference (compare two numbers). When you see \(a-b\), you can think: start at \(a\) and remove \(b\). On a number line, subtraction is like hopping backward.
Inverse relationship
Addition and subtraction are inverse operations. If \(a-b=c\), then you can check with addition: \(c+b=a\).
Worked example
Example: \(18-4\)
Count back 4: \(18\to 17\to 16\to 15\to 14\). So, \(18-4=14\). Check: \(14+4=18\).
Try it
Try it 1: Compute \(14-6\).
Hint: \(14-6\) means remove 6 from 14 (or find the difference between 14 and 6).
Try it 2: Which addition sentence checks \(13-9=4\)?
Hint: If \(13-9=4\), then \(4+9\) must equal 13.
Summary
\(a-b\) can mean take away or find the difference.
Check subtraction with addition: if \(a-b=c\), then \(c+b=a\).
Facts & Strategies
Fast strategies for addition and subtraction facts
Learning goal: Use mental math strategies (not guessing) to add and subtract quickly and accurately.
Key strategies
+0 / -0: the number stays the same
Make a ten: move to 10 (or the next ten) first
Doubles: \(6+6\), \(7+7\), \(8+8\)
Near doubles: \(7+8\) is one more than \(7+7\)
Bridge tens: for example, \(28+7 = 28+2+5 = 30+5\)
Compensation: adjust, then fix (for example, \(52-19 = 52-20+1\))
Worked example
Example: \(9+7\)
Make a ten: \(9+7=(9+1)+6=10+6=16\).
Try it
Try it 1: Compute \(8+7\).
Hint: Use near doubles: \(8+7\) is one less than \(8+8\).
Try it 2: Compute \(100-45\).
Hint: Subtract tens and ones: \(100-40=60\), then \(60-5=55\).
Summary
Use strategies like make-a-ten, doubles, and compensation.
Good mental math is step-by-step, not guessing.
Regrouping
Multi-digit addition and subtraction with regrouping
Learning goal: Use place value and regrouping (carrying/borrowing) to add and subtract two-digit numbers accurately.
Key idea
Line up digits by place value (ones under ones, tens under tens). For addition, if the ones add to 10 or more, regroup 10 ones as 1 ten. For subtraction, if you cannot subtract in the ones place, regroup 1 ten as 10 ones.
Align by place value. Ones: \(6+8=14\) → write 4, carry 1 ten. Tens: \(3+4+1=8\). So \(36+48=84\).
Try it 2: Compute \(64-39\).
Hint: Regroup: \(64\) becomes \(50+14\). Then \(14-9=5\) and \(50-30=20\). Total \(25\).
Summary
Use place value alignment to avoid mistakes.
Regroup when needed (carry in addition, borrow in subtraction).
Multi-step
Multi-step addition and subtraction (left to right)
Learning goal: Evaluate expressions with \(+\) and \(-\) by working carefully from left to right.
Key idea
Addition and subtraction have the same priority. When an expression has only \(+\) and \(-\), you work from left to right (after you do anything inside parentheses).
Worked example
Example: \(18-6+3\)
Step 1: \(18-6=12\). Step 2: \(12+3=15\). So, \(18-6+3=15\).
Try it
Try it: Compute \(25+15-30\).
Hint: Add first: \(25+15=40\). Then subtract: \(40-30\).
Worked solution
Work left to right: \(25+15=40\). \(40-30=10\). So, \(25+15-30=10\).
Summary
With only \(+\) and \(-\), work left to right.
Show steps to avoid common sign mistakes.
Check & Missing Numbers
Check your work and solve missing-number equations
Learning goal: Use inverse operations to find unknowns and check answers confidently.
Key idea
If a number is missing, use the inverse operation:
If \(x+b=a\), then \(x=a-b\).
If \(a-x=b\), then \(x=a-b\).
This is also a great way to check subtraction with addition (and addition with subtraction).
Worked example
Example: Find \(x\) in \(x+9=16\)
Use subtraction: \(x = 16-9 = 7\). Check: \(7+9=16\).
Try it
Try it 1: Solve \(?\,+8=14\).
Hint: Use subtraction: \(14-8\).
Try it 2: Solve \(20-?=5\).
Hint: If \(20-?=5\), then \(?=20-5\).
Summary
Use inverse operations to find missing numbers.
Always check: a quick check prevents small mistakes from becoming big ones.
Applications & History
Why addition and subtraction matter
Learning goal: Connect addition and subtraction to real life: totals, change, distance, time, and comparing values.
Where you use addition and subtraction
Money: totals and change (paying and getting change back).
Distance and time: how far, how long, and how much remains.
Temperature: increases and decreases (differences between readings).
Data: comparing values to find the difference.
Geometry:perimeter is found by adding side lengths.
Worked example: making change
Example: You pay 20 and the cost is 8.
Change = \(20-8=12\). Answer: The change is 12.
Try it
Try it 1: You have 15 stickers. You give away 7. How many stickers are left?
Hint: "Give away" means subtract: \(15-7\).
Fun facts (a little history)
Symbols: The plus sign \(+\) and minus sign \(-\) are used worldwide to show addition and subtraction.
More meanings: The minus sign can also show a negative number (for example, \(-3\)).
Mental math: Before calculators, people relied on smart strategies (like making tens) to add and subtract quickly.
Try it 2: Which symbol means subtraction?
Hint: The minus sign \(-\) means subtract (or indicates a negative number).
Final recap
Addition combines parts to make a total: \(a+b\).
Subtraction removes or compares to find a difference: \(a-b\).
Use strategies (make ten, doubles, compensation) to be fast and accurate.
Use place value and regrouping for multi-digit problems.
Check your answers using inverse operations.
Next step: Close this lesson and try your quiz again. If you miss a question, reopen the book and review the page that matches the skill.
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