This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, two strategies are compared for efficiency, and the question asks which is best for subtraction and why. To analyze, compare (counting back efficient for 58-55 because small difference means few counts: 57,56,55=3; break apart also works but more steps for simple problem). Choice B is correct because counting back is best strategy for 58-55 (subtracting 3 is quick, just 57,56,55), demonstrating understanding of efficiency comparison. Choice A represents a specific error (wrong efficiency judgment, said break apart best with incorrect reason "must regroup" when no regrouping needed here), which typically happens when students misjudge efficiency. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using counting back. From 58, back 1 to 57, back to 56, back to 55—that's 3.' Show same problem solved multiple ways, compare: 'For 58-55, counting back (3 counts), or break apart (50-50=0, 8-5=3—also quick). Which is faster? Counting back for small numbers!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'One used counting back, another break apart. Both got 3. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, a partial make ten strategy is shown, and the question asks to complete the blanks. To analyze, examine steps (for 47+6, decompose 6 into 3+3 to make 47+3=50, then 50+3=53). Choice A is correct because the blanks are 3 and 3 (splitting 6 to make next ten at 50), demonstrating understanding of mathematical reasoning. Choice C represents a specific error (incorrect split like 2 and 4 which wouldn't make 50 from 47), which typically happens when students don't understand strategy characteristics. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. 47+6: Need 3 to 50, break 6 into 3+3, 50+3=53.' Show same problem solved multiple ways, compare: 'Make ten vs. others.' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Correct split. Why?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Each strategy has strengths—counting on quick for small numbers, break apart good for larger, make ten leverages 10 as friendly number. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, student work is shown and question asks which strategy was used. To analyze, examine steps in work (if counting by ones = counting on; if making 10 first = make ten; if separating tens and ones = break apart). Choice B is correct because the work shown uses make ten strategy (decomposed 8 into 3+5 to make 47+3=50 first, then 50+5=55). This demonstrates understanding of strategy characteristics. Choice A represents wrong strategy identified (said counting on when work clearly shows make ten—no simple counting by ones from 47). This error typically happens when students don't understand strategy characteristics. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. I have 8, I need 2 more to make 10. So I break 5 into 2 and 3. Now I have 10 + 3 = 13.' Show same problem solved multiple ways, compare: 'For 47+3, I could count on (48, 49, 50—quick!), or use standard algorithm (write vertically, add—more work). Which is faster? Counting on!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Emma used make ten, Jamal used break apart. Both got 13. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like $47+3$); (2) Make ten—decompose to make 10 first ($8+5 \rightarrow 8+2+3 \rightarrow 10+3=13$; best when number close to 10); (3) Break apart—separate tens and ones, add separately ($47+28 \rightarrow 40+20=60, 7+8=15, 60+15=75$; best for two-digit numbers); (4) Compensation—adjust to friendly number ($47+28 \rightarrow 50+28-3=78-3=75$; good for numbers near decades); (5) Counting back/up for subtraction. Each strategy has strengths—counting on quick for small numbers, break apart good for larger, make ten leverages 10 as friendly number. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, the question asks to complete make ten steps. To analyze, examine steps ($8+7$ decomposed as $8+2$ to make 10, remaining 5). Choice B is correct because to make ten from 8 you need 2, leaving 5 from 7 ($10+5=15$), demonstrating understanding of strategy characteristics. Choice A represents specific error (wrong decomposition—2 would be repeating the 2 without leaving remainder). This error typically happens when students confuse strategy names and methods. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. I have 8, I need 2 more to make 10. So I break 5 into 2 and 3. Now I have 10 + 3 = 13.' Show same problem solved multiple ways, compare: 'For $47+3$, I could count on (48, 49, 50—quick!), or use standard algorithm (write vertically, add—more work). Which is faster? Counting on!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Emma used make ten, Jamal used break apart. Both got 13. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Each strategy has strengths—counting on quick for small numbers, break apart good for larger, make ten leverages 10 as friendly number. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, the question asks to complete make ten steps. To analyze, examine steps (8+7 decomposed as 8+2 to make 10, remaining 5). Choice B is correct because to make ten from 8 you need 2, leaving 5 from 7 (10+5=15), demonstrating understanding of strategy characteristics. Choice A represents specific error (wrong decomposition—2 would be repeating the 2 without leaving remainder). This error typically happens when students confuse strategy names and methods. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. I have 8, I need 2 more to make 10. So I break 5 into 2 and 3. Now I have 10 + 3 = 13.' Show same problem solved multiple ways, compare: 'For 47+3, I could count on (48, 49, 50—quick!), or use standard algorithm (write vertically, add—more work). Which is faster? Counting on!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Emma used make ten, Jamal used break apart. Both got 13. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, student work with an error is shown, and the question asks what mistake was made in attempting make ten. To analyze, examine steps in work (she added extra 2 without properly splitting 7, so got 17 instead of 15; correct split is 7 into 2+5 for 8+2=10+5=15). Choice C is correct because she split 7 wrong (it should be 2 and 5, but she added full 7 after 2, leading to extra 2), demonstrating understanding of strategy characteristics. Choice B represents a specific error (missed error, said forgot to subtract which confuses addition strategy), which typically happens when students don't recognize strategy from work shown. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. 8+7: Break 7 into 2+5, 8+2=10, 10+5=15.' Show same problem solved multiple ways, compare: 'Correct make ten vs. error—which is right?' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Maya made a mistake. Why?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Each strategy has strengths—counting on quick for small numbers, break apart good for larger, make ten leverages 10 as friendly number. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, asks best strategy for specific problem. To analyze, compare (counting up efficient for 92-89 because numbers are close—only 3 counts). Choice B is correct because counting up is best strategy for 92-89 because it's quick (count 90,91,92—3 steps to find difference). This demonstrates understanding of efficiency comparison. Choice A represents wrong efficiency judgment (said break apart best when counting up is faster for close numbers—no need to separate tens and ones). This error typically happens when students misjudge efficiency. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. I have 8, I need 2 more to make 10. So I break 5 into 2 and 3. Now I have 10 + 3 = 13.' Show same problem solved multiple ways, compare: 'For 47+3, I could count on (48, 49, 50—quick!), or use standard algorithm (write vertically, add—more work). Which is faster? Counting on!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Emma used make ten, Jamal used break apart. Both got 13. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Each strategy has strengths—counting on quick for small numbers, break apart good for larger, make ten leverages 10 as friendly number. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, student work is shown and question asks which strategy was used. To analyze, examine steps in work (if counting by ones = counting on; if making 10 first = make ten; if separating tens and ones = break apart). Choice C is correct because the work shown uses counting up strategy (counted from 47 up to 55 to find the difference of 8). This demonstrates understanding of strategy characteristics. Choice A represents wrong strategy identified (said counting back when work clearly shows counting up—no backward counting). This error typically happens when students confuse strategy names and methods. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. I have 8, I need 2 more to make 10. So I break 5 into 2 and 3. Now I have 10 + 3 = 13.' Show same problem solved multiple ways, compare: 'For 47+3, I could count on (48, 49, 50—quick!), or use standard algorithm (write vertically, add—more work). Which is faster? Counting on!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Emma used make ten, Jamal used break apart. Both got 13. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Each strategy has strengths—counting on quick for small numbers, break apart good for larger, make ten leverages 10 as friendly number. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, two strategies compared for efficiency. To analyze, compare (counting on efficient for 47+3 because only 3 counts; break apart better for 47+28 because too many counts otherwise). Choice B is correct because number line jumps is more efficient than counting on for 47+28 because you can jump tens then ones (jump +20, then +8—quick). This demonstrates understanding of efficiency comparison. Choice A represents wrong efficiency judgment (said counting on best for 47+28 when this would require 28 counts—inefficient compared to break apart or number line jumps). This error typically happens when students misjudge efficiency. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. I have 8, I need 2 more to make 10. So I break 5 into 2 and 3. Now I have 10 + 3 = 13.' Show same problem solved multiple ways, compare: 'For 47+3, I could count on (48, 49, 50—quick!), or use standard algorithm (write vertically, add—more work). Which is faster? Counting on!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Emma used make ten, Jamal used break apart. Both got 13. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.

This question tests 2nd grade understanding of addition and subtraction strategies, including explaining why strategies work, comparing strategies, and selecting appropriate strategies for different problems (CCSS 2.NBT.B.9: Explain why addition and subtraction strategies work, using place value and the properties of operations). Common 2nd grade strategies include: (1) Counting on—start at larger number, count up by smaller (best for adding small numbers like 47+3); (2) Make ten—decompose to make 10 first (8+5 → 8+2+3 → 10+3=13; best when number close to 10); (3) Break apart—separate tens and ones, add separately (47+28 → 40+20=60, 7+8=15, 60+15=75; best for two-digit numbers); (4) Compensation—adjust to friendly number (47+28 → 50+28-3=78-3=75; good for numbers near decades); (5) Counting back/up for subtraction. Each strategy has strengths—counting on quick for small numbers, break apart good for larger, make ten leverages 10 as friendly number. Strategies work because they use place value (break apart), number relationships (make ten), or counting principles (counting on/back). Understanding why helps students choose and apply strategies flexibly. In this problem, asks why break apart works. To analyze, explain reasoning (break apart works because uses place value). Choice B is correct because break apart works because it uses tens with tens and ones with ones (30+20=50, 4+5=9, 50+9=59). This demonstrates understanding of mathematical reasoning. Choice A represents incorrect reasoning (said it always makes a ten first which is wrong—we separate by place value, not necessarily making ten). This error typically happens when students give surface-level explanations without mathematical reasoning. To help students: Explicitly teach and name strategies. Model each strategy with think-aloud: 'I'm using make ten. I have 8, I need 2 more to make 10. So I break 5 into 2 and 3. Now I have 10 + 3 = 13.' Show same problem solved multiple ways, compare: 'For 47+3, I could count on (48, 49, 50—quick!), or use standard algorithm (write vertically, add—more work). Which is faster? Counting on!' Discuss when each strategy works best: counting on for small addends, break apart for two-digit, make ten when close to 10/decade. Use number lines to show counting strategies visually. Have students explain their thinking: 'How did you solve this? Why did you choose that strategy?' Teach error checking within strategies (recount, check if makes sense). Compare student work: 'Emma used make ten, Jamal used break apart. Both got 13. Why did both work?' Practice strategy selection: 'For this problem, which strategy makes most sense?' Build flexibility—multiple strategies often work, but efficiency varies. Watch for: naming strategies without understanding why they work, claiming one strategy always best (it depends on problem), weak mathematical explanations ("because it's easier" instead of reasoning about place value or number relationships), confusing strategy names, selecting inefficient strategies for problem type.