Emma is using the distributive property: $$48 \times 35 = (40 + 8) \times(30 + 5)$$. She calculated three of the four partial products but missed $$8 \times 5 = 40$$. The complete calculation is $$1,200 + 200 + 240 + 40 = 1,680$$. Choice B has the correct missing partial product but wrong final sum. Choice C identifies the wrong missing partial product. Choice D completely misunderstands the partial products method.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (456 = 400 + 50 + 6), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To find total widgets as 2,305 × 7, students can use the standard algorithm with regrouping or break into partial products by place value, demonstrating understanding of place value in multiplication. Choice A is correct because using the standard algorithm: 5 × 7 = 35 (write 5, carry 3), 0 × 7 = 0 + 3 = 3 (write 3), 3 × 7 = 21 (write 1, carry 2), 2 × 7 = 14 + 2 = 16 (write 16), resulting in 16,135. This demonstrates fluent multiplication using place value understanding. Choice B represents a carrying error in the hundreds place, which happens when students forget to add the carried amount. To help students: Use graph paper to align place values in standard algorithm. For partial products, explicitly break numbers by place value (2,305 = 2,000 + 300 + 5) and multiply each part, labeling (2,000 × 7 = 14,000, 300 × 7 = 2,100, 5 × 7 = 35, sum = 16,135). Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, adding factors instead of multiplying, forgetting to add all partial products, misaligning place values, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (456 = 400 + 50 + 6), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To find total widgets as 2,305 × 7, students can use the standard algorithm with regrouping or break into partial products by place value, demonstrating understanding of place value in multiplication. Choice A is correct because using the standard algorithm: 5 × 7 = 35 (write 5, carry 3), 0 × 7 = 0 + 3 = 3 (write 3), 3 × 7 = 21 (write 1, carry 2), 2 × 7 = 14 + 2 = 16 (write 16), resulting in 16,135. This demonstrates fluent multiplication using place value understanding. Choice B represents a carrying error in the hundreds place, which happens when students forget to add the carried amount. To help students: Use graph paper to align place values in standard algorithm. For partial products, explicitly break numbers by place value (2,305 = 2,000 + 300 + 5) and multiply each part, labeling (2,000 × 7 = 14,000, 300 × 7 = 2,100, 5 × 7 = 35, sum = 16,135). Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, adding factors instead of multiplying, forgetting to add all partial products, misaligning place values, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (456 = 400 + 50 + 6), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To multiply 4,096 × 8, students can use the standard algorithm with regrouping or break into partial products by place value, demonstrating understanding of place value in multiplication. Choice A is correct because using the standard algorithm: 6 × 8 = 48 (write 8, carry 4), 9 × 8 = 72 + 4 = 76 (write 6, carry 7), 0 × 8 = 0 + 7 = 7 (write 7), 4 × 8 = 32 (write 32), resulting in 32,768. This demonstrates fluent multiplication using place value understanding. Choice B represents a carrying error in the tens place, which happens when students misalign place values when adding partial products. To help students: Use graph paper to align place values in standard algorithm. For partial products, explicitly break numbers by place value (4,096 = 4,000 + 90 + 6) and multiply each part, labeling (4,000 × 8 = 32,000, 90 × 8 = 720, 6 × 8 = 48, sum = 32,768). Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, adding factors instead of multiplying, forgetting to add all partial products, misaligning place values, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (456 = 400 + 50 + 6), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To find total miles for 286 miles × 4 days, students can use the standard algorithm with regrouping or break into partial products by place value, demonstrating understanding of place value in multiplication. Choice B is correct because using the standard algorithm: 4 × 6 = 24 (write 4, carry 2), 4 × 8 = 32 + 2 = 34 (write 4, carry 3), 4 × 2 = 8 + 3 = 11 (write 11), resulting in 1,144. This demonstrates fluent multiplication using place value understanding. Choice C represents adding instead of multiplying, which happens when students confuse operations. To help students: Use graph paper to align place values in standard algorithm. For partial products, explicitly break numbers by place value (286 = 200 + 80 + 6) and multiply each part, labeling (200 × 4 = 800, 80 × 4 = 320, 6 × 4 = 24, sum = 1,144). Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, adding factors instead of multiplying, forgetting to add all partial products, misaligning place values, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (2,135 = 2,000 + 100 + 30 + 5), multiply each part separately, then add. For multi-digit numbers, the standard algorithm involves multiplying each digit by the one-digit number, regrouping as needed, and aligning by place value. Visual models like arrays help show multiplication as repeated addition. To find the total crayons in 8 boxes of 2,135 each, students can multiply 2,135 × 8 using the standard algorithm with regrouping or break into partial products by place value. Choice A is correct because using the standard algorithm: 5 × 8 = 40 (write 0, carry 4), 3 × 8 = 24 + 4 = 28 (write 8, carry 2), 1 × 8 = 8 + 2 = 10 (write 0, carry 1), 2 × 8 = 16 + 1 = 17 (write 17), resulting in 17,080, demonstrating fluent multiplication using place value understanding. Choice B represents not carrying in the thousands place, which happens when students forget to add the carried amount. To help students: Use graph paper to align place values in the standard algorithm. For partial products, explicitly break numbers by place value (2,135 = 2,000 + 100 + 30 + 5) and multiply each part, labeling (2,000 × 8 = 16,000, 100 × 8 = 800, 30 × 8 = 240, 5 × 8 = 40, sum = 17,080). Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in the standard algorithm, adding instead of multiplying, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (456 = 400 + 50 + 6), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To multiply 63 × 24, students can use the standard algorithm with regrouping or an area model showing (60 + 3) × (20 + 4), demonstrating understanding of place value in multiplication. Choice A is correct because using partial products: (60 × 20 = 1,200, 60 × 4 = 240, 3 × 20 = 60, 3 × 4 = 12), sum = 1,512. This demonstrates fluent multiplication using place value understanding. Choice B represents not carrying when regrouping needed, which happens when students forget to carry when product ≥ 10 in a place. To help students: For 2-digit × 2-digit, the area model helps visualize: draw rectangle divided into four sections (tens × tens, tens × ones, ones × tens, ones × ones), find each area, add together. Connect to arrays: 63 × 24 means 63 rows of 24 items. Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, adding factors instead of multiplying, forgetting to add all partial products, misaligning place values, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (456 = 400 + 50 + 6), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To multiply 58 × 34, students can use the standard algorithm with regrouping or an area model showing (50 + 8) × (30 + 4), demonstrating understanding of place value in multiplication. Choice B is correct because using partial products: (50 × 30 = 1,500, 50 × 4 = 200, 8 × 30 = 240, 8 × 4 = 32, sum = 1,972). This demonstrates fluent multiplication using place value understanding. Choice A represents a basic fact error in multiplying 8 × 4, which happens when students have weak basic facts. To help students: Use graph paper to align place values in standard algorithm. For 2-digit × 2-digit, the area model helps visualize: draw rectangle divided into four sections (tens × tens, tens × ones, ones × tens, ones × ones), find each area, add together. Connect to arrays: 58 × 34 means 58 rows of 34 items. Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, adding factors instead of multiplying, forgetting to add all partial products, misaligning place values, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (63 = 60 + 3, 45 = 40 + 5), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To multiply 63 × 45, students can use the standard algorithm with regrouping or an area model showing (60 + 3) × (40 + 5). Choice C is correct because using partial products: (60 × 40 = 2,400, 60 × 5 = 300, 3 × 40 = 120, 3 × 5 = 15, sum = 2,835), demonstrating fluent multiplication using place value understanding. Choice A represents a calculation error in partial products, such as misadding, which happens when students complete part of the process but not the final step. To help students: For 2-digit × 2-digit, the area model helps visualize: draw rectangle divided into four sections (tens × tens, tens × ones, ones × tens, ones × ones), find each area, add together. Connect to arrays: 63 × 45 means 63 rows of 45 items. Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, misaligning place values when adding partial products, and weak basic multiplication facts preventing fluency.

This question tests 4th grade ability to multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and properties of operations (CCSS.4.NBT.5). Multiplication can be understood using place value strategies like the partial products method, where you break numbers into place values (456 = 400 + 50 + 6), multiply each part separately, then add. For 2-digit × 2-digit, you can use the standard algorithm (multiply by ones digit, then tens digit, aligning by place value) or an area model (break rectangle into smaller sections). Visual models like rectangular arrays and area models help show how multiplication works by organizing quantities into rows and columns or length and width. To find the truck cost as 3 times $4,208, students can use the standard algorithm with regrouping or break into partial products by place value, demonstrating understanding of place value in multiplication. Choice A is correct because using the standard algorithm: 8 × 3 = 24 (write 4, carry 2), 0 × 3 = 0 + 2 = 2 (write 2), 2 × 3 = 6 (write 6), 4 × 3 = 12 (write 12), resulting in $12,624. This demonstrates fluent multiplication using place value understanding. Choice B represents not carrying in the ones place, which happens when students forget to carry when the product is 10 or more. To help students: Use graph paper to align place values in standard algorithm. For partial products, explicitly break numbers by place value (4,208 = 4,000 + 200 + 8) and multiply each part, labeling (4,000 × 3 = 12,000, 200 × 3 = 600, 8 × 3 = 24, sum = 12,624). Ensure students understand multiplication as repeated addition or equal groups. Watch for: not carrying in standard algorithm, adding factors instead of multiplying, forgetting to add all partial products, misaligning place values, and weak basic multiplication facts preventing fluency.