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 4 tens, 0 ones; 43 has 4 tens, 3 ones
40 has 0 tens, 4 ones; 43 has 0 tens, 43 ones
40 has 4 tens, 4 ones; 43 has 4 tens, 3 ones
40 has 3 tens, 0 ones; 43 has 4 tens, 0 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.
Amir shows 90 as 9 tens and 0 ones. 90 is ___ tens and ___ ones.
9 tens and 9 ones
9 tens and 0 ones
10 tens and 0 ones
0 tens and 9 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, 90 is 9 tens and 0 ones, which we can see by showing 9 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 90 represented with 9 ten-rods and no unit cubes. Choice A is correct because 90 is composed of 9 tens and 0 ones, following the decade pattern. Choice D is a common error where students include ones when there are none (9 tens and 9 ones for 90); 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 (90 vs 99: both have 9 tens, but 99 also has 9 ones); write equations showing 9 tens + 0 ones = 90; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Keisha has 30 as 3 tens and 0 ones. How is 30 different from 35?
30 has 1 ten and 3 ones, but 35 has 3 tens
30 has 30 tens, but 35 has 3 tens
30 has 0 ones, but 35 has 5 ones
30 has 3 ones, but 35 has 0 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, 30 is 3 tens and 0 ones, while 35 is 3 tens and 5 ones; the digit in the tens place tells us how many tens, and the ones place differs by having 0 or more. The stimulus shows 30 represented with 3 ten-rods and no unit cubes, compared to 35. Choice B is correct because 30 has 0 ones, but 35 has 5 ones, highlighting the key difference in the ones place. Choice A is a common error where students reverse the ones for each number (says 30 has 3 ones and 35 has 0); this happens because place value is abstract and students overlook the 0 in ones place for decades. 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 35: both have 3 tens, but 35 also has 5 ones); write equations showing 3 tens + 0 ones = 30 vs 3 tens + 5 ones = 35; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Maya has 70 as 7 bundles of 10 and 0 loose ones. 70 is how many tens?
0
7
8
70
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, 70 is 7 tens and 0 ones, which we can see by showing 7 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 70 represented with 7 bundles of 10 sticks and no loose sticks. Choice B is correct because 70 is composed of 7 tens and 0 ones, shown by 7 bundles. Choice C is a common error where students count the total value instead of number of tens (says 70 = 70 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 (70 vs 77: both have 7 tens, but 77 also has 7 ones); write equations showing 7 tens + 0 ones = 70; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.
Look at 40 shown as 4 ten-rods and 0 ones. 40 is ___ tens and ___ ones.
3 tens and 0 ones
0 tens and 4 ones
4 tens and 0 ones
4 tens and 4 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, which we can see by showing 4 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 40 represented with 4 ten-rods and no unit cubes. Choice A is correct because 40 is composed of 4 tens and 0 ones, following the decade pattern. Choice D is a common error where students include ones when there are none (4 tens and 4 ones for 40); 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 (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.
Look at 80 shown with 8 ten-rods and 0 ones. How many ones are in 80?
0
8
10
80
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, 80 is 8 tens and 0 ones, which we can see by showing 8 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 80 represented with 8 ten-rods and no unit cubes. Choice C is correct because 80 is composed of 8 tens and 0 ones, shown by 8 ten-rods. Choice A is a common error where students reverse tens and ones (think 8 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 (80 vs 88: both have 8 tens, but 88 also has 8 ones); write equations showing 8 tens + 0 ones = 80; use place value charts highlighting the 0 in ones place; have students build each decade with blocks.