- Jake makes an array of toy cars with 2 rows and 5 columns. His sister Emma makes an array of toy cars with 3 rows and 2 columns. How many more cars does Jake have than Emma?
Answer: Jake has 4 more cars than Emma
Jake's array: 2 rows × 5 columns = 5+5=10 cars. Emma's array: 3 rows × 2 columns = 2+2+2=6 cars. The difference is 10−6=4, so Jake has 4 more cars. Choice B gives the number of Emma's cars instead of the difference. Choice C subtracts the dimensions incorrectly. Choice D reverses who has more. - A tray of muffins is arranged in 3 rows with 4 muffins in each row. How many muffins are there in all?
Answer: 12
The tray has 3 rows with 4 muffins in each row, so 4 + 4 + 4 = 12 muffins in all, making Choice A correct. Choice B is wrong because it only counts one row. Choice C is wrong because it adds one extra muffin beyond the actual total. Choice D is wrong because it does not account for all three rows. - There are 5 rows of chairs with 4 chairs in each row. How many chairs are there in all?
Answer: 20
There are 20 chairs in all, since 5 rows of 4 chairs means 5 times 4, which is 20. Choosing 9 adds the number of rows and chairs per row instead of multiplying them. Choosing 4 only counts the chairs in a single row. Choosing 21 comes from a small counting error, one more than the correct total.
- Refer to the figure. Ben arranged his toy cars in an array. Which equation shows the total number of cars as a sum of equal addends?
Answer: 5+5+5+5=20
When you see an array in math, think of it as objects arranged in equal rows and equal columns. This is the foundation of multiplication, and it also connects to repeated addition — adding the same number several times. The trick is to count how many are in each row, then add that number once for every row (or count each column and add once for every column).
Since the array shows 4 rows with 5 cars in each row, you can write the total as 5+5+5+5=20. That's four addends of 5, which matches choice C. You could also think of it as 5 columns of 4, giving 4+4+4+4+4=20 — but that's not an option that matches this arrangement description exactly for the rows.
Choice A (4+5=9) is wrong because the addends aren't equal — repeated addition requires the same number each time. Choice B (4+4+4+4+4=20) does equal 20, but it uses five 4s, which would describe 5 rows of 4, not the array shown. Choice D (5+5+5=15) only adds three 5s, missing a row and giving the wrong total.
Tip: For array questions, always ask yourself two things: "How many are in each row?" and "How many rows are there?" The first number is what you add; the second is how many times you add it. - There are 3 rows of diamonds, with 4 diamonds in each row. How many diamonds are there in all?
Answer: 12
Multiplying 3 rows by 4 diamonds in each row gives 12 diamonds in all. Choice A, 4, only counts the diamonds in a single row. Choice B, 7, could come from miscounting rather than multiplying. Choice C, 11, is off by one from the correct total.
- Choose an addition equation that matches the array shown.
Answer: 4+4+4+4=16
This question tests 2nd grade understanding of using arrays to represent and solve equal groups problems, including writing repeated addition equations and finding totals (foundation for CCSS 3.OA.C.7: understanding multiplication by relating equal groups to arrays, though 2nd grade focuses on repeated addition representation of arrays). An array is a set of objects arranged in equal rows and columns. Each row contains the same number of objects (equal groups). To find the total, add the number in each row repeatedly. Example: 3 rows of 4 means 3 equal groups with 4 in each group. Write as repeated addition: 4 + 4 + 4 = 12 (adding 4 three times, once for each row). Or count by 4s: 4, 8, 12 (skip counting by the group size). Arrays show multiplication visually: 3 rows of 4 is foundation for 3 × 4 = 12 (3 groups of 4 equals 12). In this problem, the array shows 4 rows with 4 objects in each row, and students must write repeated addition for the array. To solve, write repeated addition (4+4+4+4=16). Choice B is correct because repeated addition equation 4+4+4+4=16 correctly shows 4 groups of 4. This demonstrates understanding of arrays as equal groups and using repeated addition or skip counting to find totals. Choice D represents miscounted total (said 15 instead of 16—counting error). This error typically happens when students miscount objects. To help students: Use hands-on arrays with physical objects (counters, tiles, buttons) arranged in rows. Model: 'Let's make 3 rows. Each row has 4 objects. Row 1: 4, Row 2: 4, Row 3: 4. How many in all? Let's add: 4+4+4=12!' Teach terminology: 'Rows go across (horizontal). Columns go up and down (vertical). All rows have the same number—that's equal groups.' Practice skip counting: 'Count by 4s—4, 8, 12.' Connect to real world: egg cartons (2 rows of 6), desks in classroom (4 rows of 5), muffin tins. Draw arrays: 'Show 3 rows of 4 dots.' Write repeated addition: 'This array is 4+4+4 because we have 4 in each row, and 3 rows.' Introduce multiplication language gently: '3 rows of 4 is 3 groups of 4, equals 12. Later we'll write this as 3×4=12.' Practice describing arrays: show array, ask 'How many rows? How many in each row?' Rotate arrays: show 3 rows of 4 and 4 rows of 3—both equal 12! Watch for: miscounting, adding rows+objects (3+4), counting only one row, confusing rows and columns, wrong repeated addition, skip counting errors. - An array has 4 rows with 5 tiles in each row. What is the total number of tiles?
Answer: 20
There are 4 rows with 5 tiles in each row, so the total is 4 times 5, or 20 tiles. Choice B comes from counting only 4 tiles in each row instead of 5. Choice C comes from counting only 3 rows instead of 4. Choice D is far too low to match 4 full rows of 5 tiles.
- Maya arranges stickers in a rectangular array. She has 3 rows with 4 stickers in each row. Then she adds one more row with the same number of stickers. What equation shows the total number of stickers Maya has now?
Answer: 4+4+4+4=16
Maya starts with 3 rows of 4 stickers each, then adds 1 more row of 4 stickers. This gives her 4 rows total, each with 4 stickers. The equation is 4+4+4+4=16. Choice A incorrectly adds 3 + 4 + 4. Choice C uses 3 as the repeated addend instead of 4. Choice D only counts 3 rows instead of 4. - Choose an addition equation that matches the array shown.
Answer: 4+4+4=12
The array matches three groups of 4, so 4+4+4=12 represents it correctly. Choice B only adds two groups instead of the three shown. Choice C adds three groups of 3 instead of 4, giving the wrong group size. Choice D only adds two groups of 4 instead of three. - An array has 5 rows with 3 dots in each row. Which equation matches the array when you add the rows together?
Answer: 3+3+3+3+3=15
Adding the 5 rows of 3 dots gives 3+3+3+3+3=15. Choice A adds the row count and the number in each row instead of adding the rows to each other. Choice B is missing one of the 5 rows. Choice D only accounts for 2 rows instead of 5. - An array has 3 rows with 7 objects in each row. How many objects are in the array in all?
Answer: 21
The array has 3 rows with 7 objects in each row, so there are 3 times 7, or 21, objects in all. Getting 10 comes from adding 3 and 7 instead of multiplying them. Getting 28 comes from mistakenly counting 4 rows instead of 3. Getting 24 comes from mistakenly counting 8 objects in each row instead of 7.
- Maria puts her stickers in 4 equal rows. There are 4 stickers in each row. How many stickers does Maria have in all?
Answer: 16
There are 4 rows with 4 stickers in each row. Add the rows: 4 + 4 + 4 + 4 = 16 stickers. The answer 8 counts only 2 rows. The answers 10 and 6 do not match the total.
- An array has 6 rows with 2 objects in each row. How many objects are there in all?
Answer: 12
The array has 6 rows with 2 objects in each row, so adding 2 six times (2+2+2+2+2+2) gives 12 objects in all. Getting 8 mixes up the number of rows with the number of objects per row. Getting 6 counts the rows but forgets that each row has 2 objects, not 1. Getting 16 comes from adding one extra group of 2 that isn't there.
- An array has 2 rows with 5 dots in each row. Which addition equation matches the array when you add the rows together?
Answer: 5+5=10
Adding the 2 rows of 5 dots gives 5+5=10. Choice A adds the row count and the number in each row instead of adding the rows to each other. Choice B includes an extra row that isn't part of this array. Choice D adds by columns instead of by rows, which doesn't match how the stem asks for the equation to be built. - An array has 4 rows with 5 objects in each row. Which equation matches this array?
Answer: 5+5+5+5=20
The array has 4 rows with 5 objects in each row, so the matching equation is 5+5+5+5=20. Using 4+4+4+4=16 mixes up the number of rows with the number of objects per row. Using 5+5+5=15 only adds three rows instead of four. Using 4+5=9 doesn't represent repeated groups at all. - How many muffins are there in all if there are 3 rows of 4?
Answer: 12
There are 3 rows with 4 muffins in each row, so multiply 3 by 4 to get 12. Choice A, 4, is just one row's worth. Choice B, 13, is off by one from the correct total. Choice C, 7, looks like an addition of 3 and 4 instead of multiplication.
- An array has 4 rows with 3 objects in each row. If you remove the bottom row (leaving 3 rows) and then add 2 more objects to each remaining row so that every row has 5 objects, which equation represents the new total?
Answer: 5+5+5=15
After removing the bottom row, 3 rows remain, and after adding 2 more objects to each row, every row now has 5 objects, so the new total is 5+5+5=15. Using 3+3+3+3+3=15 mixes up the number of rows with the number of objects in each row. Using 4+4+4+4+4=20 keeps the original 4 rows instead of removing one. Using 3+3+3+3=12 forgets to add the 2 extra objects to each row. - Tommy creates an array with 18 total objects arranged in equal rows. Each row has the same number of objects. Which equation could represent Tommy's array?
Answer: More than one of these is correct
Since the stem doesn't say how many rows Tommy used, more than one equation could describe his array: 3 rows of 6, 6 rows of 3, or 9 rows of 2 all total 18. Choice A is incorrect because it claims only one arrangement is possible when several work. Choice B is incorrect for the same reason. Choice C is incorrect because it also wrongly rules out the other valid arrangements.
- Use the array of flowers to answer the question. Which equation does NOT give the total number of flowers?
Answer: 5+2=7
When you see an array (rows and columns of objects), you can find the total in more than one way: by adding the rows together, by adding the columns together, or by using repeated addition. Every correct equation must actually count all the flowers in the array. Picture an array with 2 rows of 5 flowers (or 5 rows of 2 flowers) — that's 10 flowers total.
Choice C shows 5+2=7, which only adds one row and one column together instead of counting all the flowers. It gives 7, not 10, so it does not represent the total. That's why C is the equation that does NOT work.
Choice A, 5+5=10, correctly adds the two rows of 5 flowers each. Choice B, 2+2+2+2+2=10, adds the five columns of 2 flowers each — another valid way to reach the total.
A helpful strategy: whenever you see an array problem, check that the equation uses repeated addition (the same number added again and again) or adds full rows/columns together. If an equation just adds one row to one column, like 5+2, it's mixing things up and missing most of the flowers. Always ask yourself: "Does this equation actually count every object?" - An array has 5 rows with 2 objects in each row. Choose an addition equation that matches the array.
Answer: 2+2+2+2+2=10
The array has 5 rows with 2 objects in each row, so the matching equation is 2+2+2+2+2=10. Using 2+2+2+2=8 only shows 4 rows instead of 5. Using 2+5=7 just adds the two numbers together instead of showing repeated groups. Using 5+5=10 swaps the rows and objects-per-row, showing 2 groups of 5 instead of 5 groups of 2.
