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Algebra Readiness · Unit 1
Addition and Subtraction Within 100
Large problems become easier when you break the numbers into useful parts. You do not have to use the same strategy every time.
Explore the Strategies58 + 27+2078+785
Why should I care?
These Strategies Help With Everyday Numbers
Use them to total prices, compare scores, find change, follow distances, and check whether an answer makes sense.
Scores
Find how many points separate two teams.
Money
Calculate a total or the change you should receive.
Distance
Follow miles traveled or remaining.
1
Strategy 1
Add Up
I can add within 100 by adding useful chunks.
Start with the larger number. Add the tens, then add the ones.
58+2078+785
58 + 27
- Break 27 into 20 and 7.
- Add the tens: 58 + 20 = 78.
- Add the ones: 78 + 7 = 85.
Core Practice AR-U1-WS8 · Questions 1–10 PDF ↓Complete Worksheet AR-U1-WS8 · Questions 1–16 PDF ↓Teacher Answer Key AR-U1-WS8 · Sign in →
REAL-LIFE PRACTICE
Add Up Practice
THE DROP Choose any two items for your cart
CHECKOUT CARTChoose 2 items
Choose two items. What is your checkout total?
2
Strategy 2
Remove or Count Back
I can subtract within 100 by removing useful chunks.
Start with the whole amount. Take away the tens, then take away the ones.
83−2063−657
83 − 26
- Break 26 into 20 and 6.
- Remove 20: 83 − 20 = 63.
- Count back 6: 63 − 6 = 57.
Core Practice AR-U1-WS9 · Questions 1–10 PDF ↓Complete Worksheet AR-U1-WS9 · Questions 1–16 PDF ↓Teacher Answer Key AR-U1-WS9 · Sign in →
REAL-LIFE PRACTICE
Remove or Count Back Practice
SALE
ORIGINAL PRICE$76
−DISCOUNT$24
NEW AMOUNT: $_____
A $76 jacket is $24 off. What is the sale price?
3
Strategy 3
Use Place Value and Negative Numbers
I can break apart tens and ones to add or subtract.
The place of a digit tells its value. In 47, the 4 means four tens, or 40. The 7 means seven ones.
Learn this first
How Place Value Works
A digit's position tells how much it is worth. Moving one place to the left makes its value 10 times greater. Moving one place to the right makes its value 10 times smaller.
In 247, the same digit does not always mean the same amount:
247=200+40+7
Important trade: 10 ones can be traded for 1 ten. Ten tens can be traded for 1 hundred. The amount stays the same.
What Does 47 Mean?
4 tens + 7 ones
Place-Value Chart
Tens440Ones77
47 = 40 + 7
Build 47
4 tens + 7 ones
Build 36
3 tens + 6 ones
Combine and Trade
7 tens + 13 ones
Trade 10 ones for 1 ten.
8 tens + 3 ones = 83A second way to think
When the Ones Make a Negative Number
In 52 − 27, the ones problem is 2 − 7. That equals −5. A negative amount means we are five short.
50 − 20 = 302 − 7 = −530 + (−5) = 25
Core Practice AR-U1-WS10 · Questions 1–10 PDF ↓Complete Worksheet AR-U1-WS10 · Questions 1–16 PDF ↓Teacher Answer Key AR-U1-WS10 · Sign in →
REAL-LIFE PRACTICE
Place Value Practice
Build $47
Use $10s for tens, $5s for a useful halfway amount, and $1s for ones.
$10 BILLS
0
$5 BILLS
0
$1 BILLS
0
Your money shows $0
Build $47 with tens and ones.
4
Strategy 4
Adjust One Number
I can change one number to make an easier problem, then fix the change.
An easy number, sometimes called a friendly number, usually ends in 0.
49 + 36Make 49 into 5050 + 36 = 86Remove the extra 185
Core Practice AR-U1-WS11 · Questions 1–10 PDF ↓Complete Worksheet AR-U1-WS11 · Questions 1–16 PDF ↓Teacher Answer Key AR-U1-WS11 · Sign in →
REAL-LIFE PRACTICE
Adjust One Number Practice
FOOTBALL SCOREBOARD
03:38
HOME39
🏈QUARTER 3
VISITORS24
How many total points are on the scoreboard?
Add the HOME and VISITORS scores. What is the total?
5
Strategy 5
Keep a Constant Difference
I can move both numbers the same amount to make subtraction easier.
The difference means the space between two numbers. If both numbers move the same amount, that space does not change.
39difference: 3372
Move both numbers up 140same difference: 3373
72 − 39 = 73 − 40 = 33Core Practice AR-U1-WS12 · Questions 1–10 PDF ↓Complete Worksheet AR-U1-WS12 · Questions 1–16 PDF ↓Teacher Answer Key AR-U1-WS12 · Sign in →
REAL-LIFE PRACTICE
Constant Difference Practice
TRIP DISTANCE
MPH65
DIGITAL TRIP ODOMETER
START000029
→END000064
Subtract the start reading from the end reading.
RPM3
The odometer started at 29 and ended at 64. Miles traveled?
6
Strategy 6
Use a Number Line
I can use jumps on a number line to add and subtract within 100.
Move right to add. Move left to subtract. Large jumps can show tens; smaller jumps can show ones.
+20
+7
58687885Use the Number Line Below
The practice keeps each problem on this page while you move along the number line. The separate full tool remains available for problems of your own.
Core Practice AR-U1-WS13 · Questions 1–10 PDF ↓Complete Worksheet AR-U1-WS13 · Questions 1–16 PDF ↓Teacher Answer Key AR-U1-WS13 · Sign in →
REAL-LIFE PRACTICE
Number Line Practice
Show 36 + 27.
Start at 36. Use the jumps to solve the problem.
3132333435363738394041424344454647484950515253545556575859606162636465666768
Current landing number: 0
Remember
Teachers may focus on one strategy at a time. You do not have to master all six strategies in one lesson. Choose the strategy that helps the numbers make sense.