9
6
0
Teacher Notes: Common Misconceptions
• Missing 0 Placeholder: If student calculates row 2 as 5,635 instead of 56,350 (Q5), remind them they are multiplying by 7 tens (70), not 7.
• Zero in Top Factor (Q5): Watch out for \( 0 \times 7 = 0 \). Students often write the carried 3 as 0 or forget to add it to the product \( (0 + 3 = 3) \).
• Premature Addition: Ensure carried numbers are added after multiplying \( (7 \times 5 = 35) \), not before.
Part 1 Max Score: 5 Points Continue to Page 2 Key →
Page 1 of 2 Exemplar • Algorithm Aces Teacher Key • Grade 5 Standard Algorithm
Teacher Exemplar
Part 2: 3-Digit × 3-Digit Answer Key & Solutions
Total: 10 / 10
Row 1: Ones partial product (0 zeros)
Row 2: Tens partial product (1 zero)
Row 3: Hundreds partial product (2 zeros)
6 243 × 132 = 32,076
Exemplar
Regroup:
1
2 4 3
× 1 3 2
4
8
6
7
2
9
0
2
4
3
0
0
3
2
0
7
6
7 415 × 264 = 109,560
Exemplar
Regroup:
3
2
4 1 5
× 2 6 4
1
6
6
0
2
4
9
0
0
8
3
0
0
0
1
0
9
5
6
0
8 538 × 347 = 186,686
Exemplar
Regroup:
2
1
2
5 3 8
× 3 4 7
3
7
6
6
2
1
5
2
0
1
6
1
4
0
0
1
8
6
6
8
6
9 672 × 508 = 341,376
Zero Multiplier
Regroup:
3
1
6 7 2
× 5 0 8
5
3
7
6
0
0
0
0
0
3
3
6
0
0
0
3
4
1
3
7
6
10 794 × 456 = 362,064
Exemplar
Regroup:
3
1
7 9 4
× 4 5 6
4
7
6
4
3
9
7
0
0
3
1
7
6
0
0
3
6
2
0
6
4
Estimation Station • Model Exemplar
Accept reasonable front-end or rounded estimates. Example for Problem 7:
Problem #: Problem 7
Rounded Factors: 400 × 300
Estimated Product: 120,000
Reasonableness Verified: Actual answer 109,560 is very close to estimate 120,000.
Page 2 of 2 Exemplar • Algorithm Aces Teacher Key • Grade 5 Standard Algorithm
Part 2: Draw Your Own Double Number Line • 5 Questions (Q5–Q9)
Drawing Section
Name:
Directions: Label both lines with units, start at 0, draw equal ticks, and circle the answer.
Score: / 5
5 Orchard Organic Fertilizer
1 batch = 3 gal compost tea : 10 lb kelp meal
The crew uses 30 pounds of kelp meal. Draw and label a double number line to find the number of batches and gallons of tea used.
Line 1: __________________ (gal) Draw tick marks • scale by 3
0
0
Line 2: __________________ (lb) Find 30 lb →
Batches:
Compost Tea: gallons
6 Farmhouse Pancake Batter
1 batch = 4 cups buttermilk : 7 cups flour
The breakfast cook uses 16 cups of buttermilk. Draw and label a double number line to find the number of batches and cups of flour needed.
Line 1: __________________ (cups) Scale by 4 • find 16 cups
0
0
Line 2: __________________ (cups) Scale by 7
Batches:
Flour: cups
7 Calf Milk Replacer
1 batch = 3 scoops powder : 8 cups warm water
The calf feeder uses 15 scoops of powder. Draw a double number line to determine how many batches were mixed and how many cups of warm water were added.
Line 1: __________________ (scoops) Scale by 3 • find 15 scoops
0
0
Line 2: __________________ (cups) Scale by 8
Batches:
Warm Water: cups
8 Honey Bee Sugar Syrup
1 batch = 5 lb cane sugar : 3 quarts water
An apiary dissolves 25 pounds of pure cane sugar for hive feeding. Draw a double number line to find the number of batches and quarts of water boiled.
Line 1: __________________ (lb) Scale by 5 • find 25 lb
0
0
Line 2: __________________ (quarts) Scale by 3
Batches:
Water: quarts
9 Barnyard Mineral Lick
1 batch = 6 lb binder clay : 9 ounces coarse salt
The livestock keeper measures 27 ounces of coarse salt. Draw a double number line to find the number of batches and pounds of binder clay needed.
Line 1: __________________ (lb) Scale by 6
0
0
Line 2: __________________ (oz) Find 27 oz →
Batches:
Binder Clay: lb
Page 2 of 2 • Batch Finder Worksheet • Grade 6 Mathematics • Questions 5 to 9
Compost Tea: 9 gallons (\(3 \times 3\))
6 Farmhouse Pancake Batter Key
1 batch = 4 c : 7 c
Buttermilk (cups): 0481216
Batches: 0b1b2b3b4 batches
Flour (cups): 07142128
Batches: 4 batches (\(16 \div 4\))
Flour: 28 cups (\(4 \times 7\))
7 Calf Milk Replacer Key
1 batch = 3 scoops : 8 c
Powder (scoops): 03691215
Batches: 0b1b2b3b4b5 batches
Water (cups): 0816243240
Batches: 5 batches (\(15 \div 3\))
Warm Water: 40 cups (\(5 \times 8\))
8 Honey Bee Sugar Syrup Key
1 batch = 5 lb : 3 qt
Sugar (lb): 0510152025
Batches: 0b1b2b3b4b5 batches
Water (quarts): 03691215
Batches: 5 batches (\(25 \div 5\))
Water: 15 quarts (\(5 \times 3\))
9 Barnyard Mineral Lick Key
1 batch = 6 lb : 9 oz
Clay Binder (lb): 061218
Batches: 0b1b2b3 batches
Coarse Salt (oz): 091827
Batches: 3 batches (\(27 \div 9\))
Clay Binder: 18 lb (\(3 \times 6\))
Page 2 of 2 Exemplar • Batch Finder Teacher Guide • Questions 5 to 9
