The Tens Digit
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1st Grade Math › The Tens Digit
Maya has 4 bundles of 10 straws, 0 loose. What number?
4
30
40
44
Explanation
This question tests 1st grade understanding that decade numbers (10, 20, 30...90) represent multiples of ten with 0 ones (CCSS.1.NBT.2.c). Decade numbers—10, 20, 30, 40, 50, 60, 70, 80, and 90—are special because they contain only tens and no ones. For example, 40 is 4 tens and 0 ones, which we can see by showing 4 bundles of 10 with no loose items; the digit in the tens place tells us how many tens, and the 0 in the ones place tells us there are no loose ones. The stimulus describes Maya with 4 bundles of 10 straws and 0 loose straws, representing 40. Choice C is correct because 40 is composed of 4 tens and 0 ones, matching the 4 bundles with no loose straws. Choice B is a common error where students include ones when there are none (4 tens and 4 ones for 44); this happens because students confuse decade structure with teen structure or reverse tens and ones. To help students: Use base-10 blocks extensively—show only ten-rods with explicit empty space where ones would be; emphasize 0 ones verbally and visually; practice counting by tens (10, 20, 30...90); connect decade numbers to skip counting; compare decades to non-decades (40 vs 44: both have 4 tens, but 44 also has 4 ones); write equations showing 4 tens + 0 ones = 40; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Sofia has 30 as 3 bundles of 10 and 0 loose sticks. How many ones?
0
3
10
30
Explanation
This question tests 1st grade understanding that decade numbers (10, 20, 30...90) represent multiples of ten with 0 ones (CCSS.1.NBT.2.c). Decade numbers—10, 20, 30, 40, 50, 60, 70, 80, and 90—are special because they contain only tens and no ones. For example, 30 is 3 tens and 0 ones, which we can see by showing 3 bundles of 10 sticks with no loose sticks; the digit in the tens place tells us how many tens, and the 0 in the ones place tells us there are no loose ones. The stimulus shows 30 represented with 3 bundles of 10 sticks and no loose sticks. Choice C is correct because 30 is composed of 3 tens and 0 ones, shown by 3 bundles. Choice A is a common error where students reverse tens and ones (think 3 ones instead of 0); this happens because the 0 in ones place is sometimes overlooked and students confuse decade structure with teen structure. To help students: Use base-10 blocks extensively—show only ten-rods with explicit empty space where ones would be; emphasize 0 ones verbally and visually; practice counting by tens (10, 20, 30...90); connect decade numbers to skip counting; compare decades to non-decades (30 vs 33: both have 3 tens, but 33 also has 3 ones); write equations showing $3 \text{ tens} + 0 \text{ ones} = 30$; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Jamal shows $60$ with ten-rods only. How many tens?
0
5
6
60
Explanation
This question tests 1st grade understanding that decade numbers (10, 20, 30...90) represent multiples of ten with 0 ones (CCSS.1.NBT.2.c). Decade numbers—10, 20, 30, 40, 50, 60, 70, 80, and 90—are special because they contain only tens and no ones. For example, 60 is 6 tens and 0 ones, which we can see by showing 6 ten-rods with no unit cubes; the digit in the tens place tells us how many tens, and the 0 in the ones place tells us there are no loose ones. The stimulus describes Jamal showing 60 with ten-rods only. Choice C is correct because 60 is composed of 6 tens and 0 ones, shown by 6 ten-rods. Choice B is a common error where students count the total value instead of number of tens (says 60 = 60 tens); this happens because place value is abstract and the total count can be confused with the number of tens. To help students: Use base-10 blocks extensively—show only ten-rods with explicit empty space where ones would be; emphasize 0 ones verbally and visually; practice counting by tens (10, 20, 30...90); connect decade numbers to skip counting; compare decades to non-decades (60 vs 66: both have 6 tens, but 66 also has 6 ones); write equations showing $6 \text{ tens} + 0 \text{ ones} = 60$; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Jamal shows 60 with 6 ten-rods and 0 ones. How many tens are in 60?
0
5
6
60
Explanation
This question tests 1st grade understanding that decade numbers (10, 20, 30...90) represent multiples of ten with 0 ones (CCSS.1.NBT.2.c). Decade numbers—10, 20, 30, 40, 50, 60, 70, 80, and 90—are special because they contain only tens and no ones. For example, 60 is 6 tens and 0 ones, which we can see by showing 6 ten-rods with no unit cubes; the digit in the tens place tells us how many tens, and the 0 in the ones place tells us there are no loose ones. The stimulus shows 60 represented with 6 ten-rods and no unit cubes. Choice A is correct because 60 contains exactly 6 tens with 0 ones. Choice C is a common error where students count the total value instead of number of tens (says 60 = 60 tens); this happens because place value is abstract and students confuse the total count with the number of tens. To help students: Use base-10 blocks extensively—show only ten-rods with explicit empty space where ones would be; emphasize 0 ones verbally and visually; practice counting by tens (10, 20, 30...90); connect decade numbers to skip counting; compare decades to non-decades (60 vs 66: both have 6 tens, but 66 also has 6 ones); write equations showing 6 tens + 0 ones = 60; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Look at 40 and 43. How are they different?
40 has 0 tens, 4 ones; 43 has 0 tens, 43 ones
40 has 3 tens, 0 ones; 43 has 4 tens, 0 ones
40 has 4 tens, 4 ones; 43 has 4 tens, 3 ones
40 has 4 tens, 0 ones; 43 has 4 tens, 3 ones
Explanation
This question tests 1st grade understanding that decade numbers (10, 20, 30...90) represent multiples of ten with 0 ones (CCSS.1.NBT.2.c). Decade numbers—10, 20, 30, 40, 50, 60, 70, 80, and 90—are special because they contain only tens and no ones. For example, 40 is 4 tens and 0 ones, while 43 is 4 tens and 3 ones; the digit in the tens place tells us how many tens, and the ones place differs by having 0 or more. The stimulus asks how 40 and 43 are different. Choice A is correct because 40 has 4 tens and 0 ones, while 43 has 4 tens and 3 ones, highlighting the difference in the ones place. Choice D is a common error where students include ones in the decade when there are none (says 40 has 4 ones); this happens because students confuse the total with place value or add extra ones. To help students: Use base-10 blocks extensively—show only ten-rods with explicit empty space where ones would be; emphasize 0 ones verbally and visually; practice counting by tens (10, 20, 30...90); connect decade numbers to skip counting; compare decades to non-decades (40 vs 43: both have 4 tens, but 43 has 3 ones); write equations showing 4 tens + 0 ones = 40 vs 4 tens + 3 ones = 43; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Ben counts by tens: $$10, 20, 30, 40, 50$$. Sarah counts the tens in each number: $$1, 2, 3, 4, 5$$. If Ben says $$80$$ next, what should Sarah say next?
Sarah should say $$6$$
Sarah should say $$8$$
Sarah should say $$10$$
Sarah should say $$80$$
Explanation
Sarah counts how many tens are in each number. Since 80 has 8 tens (8 tens and 0 ones), Sarah should say 8. Choice A continues the pattern incorrectly as 6. Choice B repeats Ben's number. Choice D gives the next multiple of ten incorrectly.
A number has $$6$$ tens and $$0$$ ones. Kim adds $$3$$ tens to this number. How many tens does the new number have?
The new number has $$6$$ tens
The new number has $$3$$ tens
The new number has $$9$$ tens
The new number has $$30$$ tens
Explanation
The original number has 6 tens (which is 60). Adding 3 tens means 6 + 3 = 9 tens total. Choice A shows only the tens added. Choice B shows only the original tens. Choice D incorrectly multiplies 6 × 3 = 18, then doubles it.
Look at the pattern: $$20, 30, 40, 50$$. The tens in these numbers are $$2, 3, 4, 5$$. If the pattern continues for two more numbers, how many tens will the last number have?
The last number will have $$60$$ tens
The last number will have $$7$$ tens
The last number will have $$6$$ tens
The last number will have $$70$$ tens
Explanation
The pattern of tens is 2, 3, 4, 5, and continues 6, 7. So the last number after two more steps will have 7 tens (which would be the number 70). Choice A gives the second-to-last number of tens. Choices C and D confuse the number of tens with the actual number value.
Lily has $$90$$ stickers arranged in groups of ten. She gives away $$30$$ stickers to her friends. How many groups of ten does she have left?
She has $$60$$ groups of ten left
She has $$6$$ groups of ten left
She has $$3$$ groups of ten left
She has $$9$$ groups of ten left
Explanation
Lily starts with 90 stickers = 9 groups of ten. She gives away 30 stickers = 3 groups of ten. So she has 9 - 3 = 6 groups of ten left. Choice B shows only the groups given away. Choice C shows the original groups. Choice D gives the remaining number of stickers, not groups.
Jake writes a number that has $$4$$ tens. Emma writes a number that has $$2$$ more tens than Jake's number. What could be Emma's number?
Emma could write $$42$$
Emma could write $$46$$
Emma could write $$24$$
Emma could write $$60$$
Explanation
Jake's number has 4 tens. Emma's number has 4 + 2 = 6 tens. The number 60 has exactly 6 tens (6 tens and 0 ones). Choice A has 4 tens, same as Jake. Choice C has 2 tens, which is 2 fewer than Jake, not 2 more. Choice D has 4 tens in the tens place but students might confuse this as having 6 total parts.