| . |
#6 Line Up & Add:
0.52 + 8.14
| O | . | t | h |
|---|---|---|---|
| . | |||
| + | . | ||
| . |
Word Problem Practice The Track Meet
Lucas ran the 50-meter sprint in 7.35 seconds. In his second race, he added 1.42 seconds to his time. What was his total time for both sprints combined?
Total Time: __________________ seconds
Show Alignment
Decimal Place Dash • Tier 1 Foundations Page 1 of 2
Tier 1 • Foundations Subtracting Decimals
Name:
Date:
STEP-BY-STEP REMINDER GUIDE: SUBTRACTING DECIMALS
1
Align Place Values
Place the larger number on top with points aligned.
2
Drop Decimal
Keep the decimal point in the exact same position.
3
Subtract Columns
Subtract hundredths first, then tenths, then ones.
Place Value Colors:
Ones (O) • Decimal Point Tenths (t) Hundredths (h)
#1 9.78 - 4.25
| O | . | t | h |
|---|---|---|---|
| 9 | . | 7 | 8 |
| - 4 | . | 2 | 5 |
| . |
#2 6.84 - 3.51
| O | . | t | h |
|---|---|---|---|
| 6 | . | 8 | 4 |
| - 3 | . | 5 | 1 |
| . |
#3 8.96 - 1.40
| O | . | t | h |
|---|---|---|---|
| 8 | . | 9 | 6 |
| - 1 | . | 4 | 0 |
| . |
#4 5.55 - 2.33
| O | . | t | h |
|---|---|---|---|
| 5 | . | 5 | 5 |
| - 2 | . | 3 | 3 |
| . |
#5 Line Up & Subtract:
7.68 - 4.12
| O | . | t | h |
|---|---|---|---|
| . | |||
| - | . | ||
| . |
#6 Line Up & Subtract:
4.97 - 0.76
| O | . | t | h |
|---|---|---|---|
| . | |||
| - | . | ||
| . |
Word Problem Practice The Science Experiment
A beaker held 9.85 ounces of liquid. Dr. Oliver poured out 4.32 ounces for a test. How many ounces of liquid remain in the beaker?
Remaining Liquid: __________________ ounces
Show Alignment
Decimal Place Dash • Tier 1 Foundations Page 2 of 2
| T | O | . | t | h |
|---|---|---|---|---|
| . | ||||
| + | . | |||
| . |
#6 Line Up & Add:
3.95 + 14.68
| T | O | . | t | h |
|---|---|---|---|---|
| . | ||||
| + | . | |||
| . |
Real-World Application The Farmers Market Grocery Bag
Elena bought apples weighing 4.75 kg, oranges weighing 3.88 kg, and grapes weighing 2.45 kg. What is the total weight of all three fruits?
Total Weight: __________________ kg
Show Your Grid Work
Decimal Place Dash • Tier 2 Precision Page 1 of 2
Tier 2 • Precision Regrouping Subtraction
Name:
Date:
STEP-BY-STEP REMINDER: BORROWING (UNGROUPING) IN DECIMALS
1
Need More Hundredths?
Borrow 1 tenth (cross out, decrease by 1). Add 10 to hundredths.
2
Need More Tenths?
Borrow 1 one across the decimal point. Add 10 to tenths.
3
Subtract New Digits
Subtract using the updated numbers in your borrow boxes.
#1 7.32 - 3.58
| O | . | t | h |
|---|---|---|---|
| 7 | . | 3 | 2 |
| - 3 | . | 5 | 8 |
| . |
#2 9.40 - 4.67
| O | . | t | h |
|---|---|---|---|
| 9 | . | 4 | 0 |
| - 4 | . | 6 | 7 |
| . |
#3 14.15 - 8.46
| T | O | . | t | h |
|---|---|---|---|---|
| 1 | 4 | . | 1 | 5 |
| - | 8 | . | 4 | 6 |
| . |
#4 20.00 - 13.48
| T | O | . | t | h |
|---|---|---|---|---|
| 2 | 0 | . | 0 | 0 |
| - 1 | 3 | . | 4 | 8 |
| . |
#5 Line Up & Subtract:
11.23 - 4.87
| T | O | . | t | h |
|---|---|---|---|---|
| . | ||||
| - | . | |||
| . |
#6 Line Up & Subtract:
8.05 - 2.68
| T | O | . | t | h |
|---|---|---|---|---|
| . | ||||
| - | . | |||
| . |
Real-World Application The School Book Fair
Jordan had a $20.00 gift card. He bought a graphic novel for $12.75 and a bookmark for $2.49. How much money is left on Jordan's gift card?
Remaining Balance: $ __________________
Show Your Steps
Decimal Place Dash • Tier 2 Precision Page 2 of 2
Multi-Step Word Problem:
4.75 + 3.88 + 2.45 = 11.08 kg
Page 2 • Subtraction with Regrouping
#1: 3.74
#2: 4.73
#3: 5.69
#4: 6.52
#5: 6.36
#6: 5.37
Multi-Step Word Problem:
$12.75 + $2.49 = $15.24 spent
$20.00 - $15.24 = $4.76 left
| Level | Alignment Criteria | Regrouping & Computation |
|---|---|---|
| 4 - Mastery | Consistently aligns decimals vertically; adds trailing zeros when needed without prompting. | Flawlessly executes regrouping across ones, tenths, and hundredths; accurate computation. |
| 3 - Proficient | Aligns decimals accurately when grid is provided; rare misalignments on horizontal format. | Regroups correctly but makes minor arithmetic calculation slips. |
| 2 - Approaching | Requires place value color cues to maintain column alignment. | Forgets to add carried digits or subtracts smaller digit from larger regardless of position. |
| 1 - Novice | Aligns numbers to right margin ignoring decimal points. | Cannot execute multi-digit regrouping with decimals; requires Tier 1 re-teaching. |
Decimal Place Dash • Complete Answer Key Page 2 of 2
| 0 | . | 5 | 2 |
| + 8 | . | 1 | 4 |
| 8 | . | 6 | 6 |
Word Problem Worked Solution 7.35 + 1.42 = 8.77 seconds
Lucas ran 7.35 seconds and added 1.42 seconds. 7.35 + 1.42 = 8.77 seconds in total.
Decimal Place Dash • Tier 1 Answer Sheet Page 1 of 2
Answer Sheet • Key Tier 1 Subtraction
ALL ANSWERS VERIFIED Full Worked Grid Models
Check Point: Top number minus bottom number column by column.
Hundredths → Tenths → Ones
#1 Answer 9.78 - 4.25
| O | . | t | h |
|---|---|---|---|
| 9 | . | 7 | 8 |
| - 4 | . | 2 | 5 |
| 5 | . | 5 | 3 |
#2 Answer 6.84 - 3.51
| O | . | t | h |
|---|---|---|---|
| 6 | . | 8 | 4 |
| - 3 | . | 5 | 1 |
| 3 | . | 3 | 3 |
#3 Answer 8.96 - 1.40
| O | . | t | h |
|---|---|---|---|
| 8 | . | 9 | 6 |
| - 1 | . | 4 | 0 |
| 7 | . | 5 | 6 |
#4 Answer 5.55 - 2.33
| O | . | t | h |
|---|---|---|---|
| 5 | . | 5 | 5 |
| - 2 | . | 3 | 3 |
| 3 | . | 2 | 2 |
#5 Answer 7.68 - 4.12
| O | . | t | h |
|---|---|---|---|
| 7 | . | 6 | 8 |
| - 4 | . | 1 | 2 |
| 3 | . | 5 | 6 |
#6 Answer 4.97 - 0.76
| O | . | t | h |
|---|---|---|---|
| 4 | . | 9 | 7 |
| - 0 | . | 7 | 6 |
| 4 | . | 2 | 1 |
Word Problem Worked Solution 9.85 - 4.32 = 5.53 ounces
The beaker started with 9.85 ounces and 4.32 ounces were removed. 9.85 - 4.32 = 5.53 ounces remain.
Decimal Place Dash • Tier 1 Answer Sheet Page 2 of 2
| t |
|---|
| h |
|---|
| 1 | 1 | 1 | ||
| 1 | 5 | . | 8 | 6 |
| + | 7 | . | 4 | 9 |
| 2 | 3 | . | 3 | 5 |
#6 Answer 3.95 + 14.68
| T | O | . | t | h |
|---|---|---|---|---|
| 1 | 1 | 1 | ||
| 3 | . | 9 | 5 | |
| + 1 | 4 | . | 6 | 8 |
| 1 | 8 | . | 6 | 3 |
Real-World Application Solution 4.75 + 3.88 + 2.45 = 11.08 kg
Elena's total fruit weight: 4.75 kg (apples) + 3.88 kg (oranges) + 2.45 kg (grapes) = 11.08 kg.
Decimal Place Dash • Tier 2 Answer Sheet Page 1 of 2
Answer Sheet • Key Tier 2 Subtraction
ALL ANSWERS VERIFIED Includes Ungrouping Borrow Steps
Check Point: Top boxes show updated values after borrowing 10 from the column to the left.
Borrow across decimal: 1 One = 10 tenths
#1 Answer 7.32 - 3.58
| O | . | t | h |
|---|---|---|---|
| 6 | 12 | 12 | |
| 7 | . | 3 | 2 |
| - 3 | . | 5 | 8 |
| 3 | . | 7 | 4 |
#2 Answer 9.40 - 4.67
| O | . | t | h |
|---|---|---|---|
| 8 | 13 | 10 | |
| 9 | . | 4 | 0 |
| - 4 | . | 6 | 7 |
| 4 | . | 7 | 3 |
#3 Answer 14.15 - 8.46
| T | O | . | t | h |
|---|---|---|---|---|
| 0 | 13 | 10 | 15 | |
| 1 | 4 | . | 1 | 5 |
| - | 8 | . | 4 | 6 |
| 5 | . | 6 | 9 |
#4 Answer 20.00 - 13.48
| T | O | . | t | h |
|---|---|---|---|---|
| 1 | 9 | 9 | 10 | |
| 2 | 0 | . | 0 | 0 |
| - 1 | 3 | . | 4 | 8 |
| 6 | . | 5 | 2 |
#5 Answer 11.23 - 4.87
| T | O | . | t | h |
|---|---|---|---|---|
| 0 | 10 | 11 | 13 | |
| 1 | 1 | . | 2 | 3 |
| - | 4 | . | 8 | 7 |
| 6 | . | 3 | 6 |
#6 Answer 8.05 - 2.68
| T | O | . | t | h |
|---|---|---|---|---|
| 7 | 9 | 15 | ||
| 8 | . | 0 | 5 | |
| - | 2 | . | 6 | 8 |
| 5 | . | 3 | 7 |
Real-World Application Solution $20.00 - $15.24 = $4.76 left
Step 1: $12.75 + $2.49 = $15.24 total spent. Step 2: $20.00 - $15.24 = $4.76 remaining.
Decimal Place Dash • Tier 2 Answer Sheet Page 2 of 2
