Monday Math Worksheet 5th Grade Math Research Log
Subject: Grade 5 Mathematics • Day 01: Monday
STATION ID: LOG-5.01
AGENT:
DATE:
Order of Operations
Evaluate using PEMDAS/GEMS:
\( 12 + (6 \times 4) \div 2 \)
Result:
\( [5 \times (8 - 3)] + 14 \)
Result:
Decimal Precision
Align the decimal points:
45.08
+ 12.9
200.5
- 84.16
The Power Multiplier
428
× 24
Scratchpad
1,506
× 35
Scratchpad
Scaling Powers
4.5 × 10
4.5 × 100
4.5 ÷ 10
4.5 ÷ 100
Field Investigations: Multi-Step
PAGE-REF: 5.01-B
INVESTIGATION A
A tech company is purchasing 24 new laptops for their designers. Each laptop costs $1,245 . They also need to buy 24 mouse pads at $12.50 each. If the company has a hardware budget of $35,000 , do they have enough money? Exactly how much will remain or how much more do they need?
Show Calculation Process (Unit Costs → Totals → Budget Check)
Total Hardware Cost
$
Final Conclusion
Yes, enough
No, not enough
Difference
$
Investigation B
Chef Rossi is preparing a massive batch of sauce. He adds 2.5 liters of water, 0.85 liters of oil, and 1.4 liters of tomato juice to a pot. During the first hour of cooking, 0.32 liters of liquid evaporates. Then, he adds another 0.5 liters of broth. What is the final volume of liquid in the pot?
Operation Sequence (Add Initial → Subtract Evaporation → Add Broth)
Final Volume: Liters
Research Challenge
"I am an expression with four terms. I contain one set of parentheses, one multiplication sign, and two addition signs. My total value is 20. If all my numbers are whole numbers between 1 and 5, what could I be?"
Expression Model:
Monday Math Key 5th Grade Answer Key
Math Research Log • Day 01: Monday
Order of Operations
\( 12 + (6 \times 4) \div 2 \)
12 + 24 ÷ 2 → 12 + 12 = 24
\( [5 \times (8 - 3)] + 14 \)
[5 × 5] + 14 → 25 + 14 = 39
Decimal Precision
45.08 + 12.90
57.98
200.50 - 84.16
116.34
Multi-Step Solutions
Investigation A (Laptops):
1. Laptops: 24 × 1,245 = $29,880
Investigation B (Sauce):
1. Initial: 2.5 + 0.85 + 1.4 = 4.75 liters
The Power Multiplier
428 × 24 = 10,272
1,506 × 35 = 52,710
Scaling Powers
45
450
0.45
0.045
Tuesday Math Worksheet 5th Grade Math Research Log
Subject: Grade 5 Mathematics • Day 02: Tuesday
STATION ID: LOG-5.02
AGENT:
DATE:
Division Terminal
Find the quotient:
12 768
Workspace
24 1,512
Workspace
Rounding Radar
Round 14.0863 to the place indicated:
Nearest Whole:
Nearest Tenth:
Nearest Hundredth:
Nearest Thousandth:
Decimal Accelerator
4.2 × 0.6 =
1.25 × 4 =
18.6 ÷ 3 =
4.8 ÷ 12 =
Field Investigations: Multi-Step
PAGE-REF: 5.02-B
INVESTIGATION A
A school garden covers 480 square feet . One-fourth of the garden is planted with tomatoes. One-third of the garden is planted with cucumbers. The remaining space is divided equally between 2 plots for peppers. How many square feet is each pepper plot ?
Phase 1: Calc Tomatoes | Phase 2: Calc Cucumbers | Phase 3: Calc Remaining | Phase 4: Divide
Total Space Used:
Each Pepper Plot: sq ft
Investigation B
Tickets for the science museum cost $14.50 for adults and $9.25 for children. A group of 3 adults and 8 children want to go. They have a coupon for $10.00 off the total price. How much will the group pay in total?
Total Adult Cost + Total Child Cost - Coupon
Final Payment: $
Research Challenge
"I am a decimal number. If you round me to the nearest tenth, I am 5.3. If you round me to the nearest whole number, I am 5. My thousandths digit is the sum of my ones and tenths digit. What number could I be?"
_ . _ _ _
Tuesday Math Key 5th Grade Answer Key
Math Research Log • Day 02: Tuesday (5th Grade)
Division Terminal
768 ÷ 12 = 64
1,512 ÷ 24 = 63
Rounding Radar
Whole: 14
Tenth: 14.1
Hundredth: 14.09
Thousandth: 14.086
Decimal Accelerator
4.2 × 0.6 = 2.52
1.25 × 4 = 5.0 (or 5)
18.6 ÷ 3 = 6.2
4.8 ÷ 12 = 0.4
Multi-Step Solutions
Problem A (Garden):
1. Tomatoes: 1/4 of 480 = 120 sq ft
Problem B (Museum):
1. Adults: 3 × 14.50 = $43.50
Research Challenge
5.257 to 5.347
One possible: 5.308 (Tenths digit 3, whole digit 5. 5+3=8 thousandths.)
Wednesday Math Worksheet 5th Grade Math Research Log
Subject: Grade 5 Mathematics • Day 03: Wednesday
STATION ID: LOG-5.03
AGENT:
DATE:
Fraction Fusion
Find the common denominator and solve:
3
4
1
6
=
5
8
-
1
3
=
State Conversion
Convert improper fractions to mixed numbers:
25/6
41/8
19/4
Equivalence Sync
FRACTION
1/2
Decimal Value
FRACTION
1/4
Decimal Value
FRACTION
3/5
Decimal Value
FRACTION
7/10
Decimal Value
Field Investigations: Multi-Step
PAGE-REF: 5.03-B
INVESTIGATION A
A recipe for giant cookies calls for 2 ½ cups of flour and 1 ¾ cups of sugar. Chef Mario wants to triple the recipe for a bake sale. How many total cups of dry ingredients (flour and sugar) will he need in all?
Method 1: (F + S) × 3 | Method 2: (F × 3) + (S × 3)
Sum of 1 Batch:
Total Dry: cups
Investigation B
A juice pitcher has 5 liters of capacity. It contains 1 ½ liters of orange juice and 2 ¾ liters of pineapple juice. How much more liquid can be added before the pitcher is completely full?
Calculate Total Current Volume → Subtract from Capacity
Space Left: Liters
Research Challenge
"I am a fraction in simplest form. My denominator is twice my numerator plus one. When you add me to 1/2, the sum is 5/6. What fraction am I?"
?
?
Wednesday Math Key 5th Grade Answer Key
Math Research Log • Day 03: Wednesday (5th Grade)
Fraction Fusion
3/4 + 1/6 → 9/12 + 2/12 = 11/12
5/8 - 1/3 → 15/24 - 8/24 = 7/24
State Conversion
25/6 = 4 ⅙
41/8 = 5 ⅛
19/4 = 4 ¾
Equivalence Sync
1/2 = 0.5
1/4 = 0.25
3/5 = 0.6
7/10 = 0.7
Multi-Step Solutions
Problem A (Bake Sale):
1. Total Flour: 2 ½ × 3 = 7 ½ cups
Problem B (Pitcher):
1. Current OJ: 1 ½ = 1 2/4 liters
Research Challenge
1/3
Checking: 1/3 + 1/2 = 2/6 + 3/6 = 5/6. Simplest form: 1/3. Denominator 3 = (2 × 1) + 1.
Thursday Math Worksheet 5th Grade Math Research Log
Subject: Grade 5 Mathematics • Day 04: Thursday
STATION ID: LOG-5.04
AGENT:
DATE:
Volume Terminal
Calculate the volume (\(V = l \times w \times h\)):
8 cm 5 cm 12 cm
Volume:
cm³
Additive Volume Challenge:
Object A: 2x3x4 | Object B: 5x5x2
Total V:
Coordinate Mapping
Plot and label the following points:
A: (2, 5) B: (0, 4) C: (4, 1) D: (3, 3)
Product Accelerator
2/3 × 4/5 =
1 ½ × 2/3 =
3/8 × 16 =
Field Investigations: Multi-Step
PAGE-REF: 5.04-B
INVESTIGATION A
A shipping company uses two sizes of boxes. Box Size A is 4 inches wide, 6 inches long, and 5 inches tall. Box Size B has twice the width and twice the length of Box A, but the same height. What is the difference in volume (in cubic inches) between one Box B and one Box A?
Phase 1: Calc Volume Box A | Phase 2: Calc New Dims for Box B | Phase 3: Calc Volume Box B | Phase 4: Find Difference
Volume Diff: in³
Investigation B
A construction project requires 15 wooden boards . Each board is 8 ¼ feet long . The contractor cuts 2 ½ feet off of every board to make them fit. What is the total length of wood (in feet) that the contractor has after making all the cuts?
Method 1: (Original - Cut) × Total Boards | Method 2: (Total Original) - (Total Cuts)
Final Length: Feet
Research Challenge
"I am a rectangular prism. My base has an area of 24 sq cm. My height is a prime number. My total volume is between 100 and 150 cubic cm. What is my height and total volume?"
Height:
Volume:
Thursday Math Key 5th Grade Answer Key
Math Research Log • Day 04: Thursday (5th Grade)
Volume Terminal
1. 8 × 5 × 12 = 480 cm³
2. Additive: (2×3×4) + (5×5×2) = 24 + 50 = 74
Coordinate Mapping
Points plotted at listed coordinates. Check (x, y) order carefully.
Product Accelerator
2/3 × 4/5 = 8/15
1 ½ × 2/3 → 3/2 × 2/3 = 6/6 = 1
3/8 × 16 = 48/8 = 6
Multi-Step Solutions
Problem A (Shipping):
1. Vol A: 4 × 6 × 5 = 120 in³
Problem B (Boards):
1. New Length: 8 ¼ - 2 ½ = 7 5/4 - 2 2/4 = 5 ¾ feet
Research Challenge
Height: 5 cm | Volume: 120 cm³
Height must be a prime number. 24 × 5 = 120 (prime 5). 24 × 3 = 72 (too low). 24 × 7 = 168 (too high).
Friday Math Worksheet 5th Grade Math Research Log
Subject: Grade 5 Mathematics • Day 05: Friday
STATION ID: LOG-5.05
AGENT:
DATE:
Division Splitting
Solve and show your model/check:
1/4 ÷ 3 =
6 ÷ 1/2 =
Quad Logic
Is the statement Always , Sometimes , or Never true?
Statement 1
"A rhombus is a square."
Statement 2
"A trapezoid is a parallelogram."
Statement 3
"A square is a rectangle."
Trend Analysis
Identify the rule and complete the data table:
Input (x) Output (y) 2 7 5 10 8 12
Equation / Rule:
y = x + ____
"Based on the table, if the input is 20, what would the output be?"
Field Investigations: Multi-Step
PAGE-REF: 5.05-B
INVESTIGATION A
A group of 5 friends is splitting the cost of a rental cabin. The total cost is $840.50 for the weekend. One friend has a loyalty credit of $45.00 that can be applied to the total. After applying the credit, how much will each friend owe if they split the remaining cost equally?
Step 1: Subtract Credit | Step 2: Divide Remainder
New Total Cost:
Each Owes: $
Investigation B
Professor Puzzler has 3 liters of chemical solution. He pours 1/2 liter into a small beaker. He divides the remaining solution equally into 10 test tubes . How many liters of solution are in each test tube ?
Calculate Remaining (Whole - Fraction) → Divide by 10
Per Tube: Liters
Weekly Summary
"Which skill from this week's research was the most difficult for you? Why? Write a tip for future agents below."
Friday Math Key 5th Grade Answer Key
Math Research Log • Day 05: Friday (5th Grade)
Division Splitting
1/4 ÷ 3 = 1/12
6 ÷ 1/2 = 12
Quad Logic
1. Rhombus is square: SOMETIMES (only if it has 90 degree angles)
2. Trapezoid is parallelogram: NEVER (trapezoid has only 1 pair parallel sides, parallelogram has 2)
3. Square is rectangle: ALWAYS (a square meets all rectangle requirements)
Trend Analysis
Table Missing Values: 8 → 13, 12 → 17
Rule: y = x + 5
If Input is 20: Output = 25
Multi-Step Solutions
Problem A (Cabin):
1. Total - Credit: 840.50 - 45.00 = $795.50
Problem B (Chemistry):
1. Remaining: 3 - 1/2 = 2.5 liters (or 2 ½)
