Grade 1 · Place Value · MAT-01-PV-002
Tens and Ones
Represent two-digit numbers as groups of tens and leftover ones.
Learning objectives
What you should be able to do
- Represent two-digit numbers as groups of tens and leftover ones.
- Explain the value of each digit in a two-digit numeral.
- Compose and decompose two-digit numbers into tens and ones in multiple representations.
Prerequisite check
Make sure the foundation is ready.
Checks Kindergarten place-value foundation.
Checks number-range familiarity.
Learn
Build the idea from meaning, not memorization.
Ten ones can be grouped as one ten
Instead of treating 34 as thirty-four separate objects, group thirty objects into three tens and leave four ones. This makes the number structure visible.
A digit's position changes its value
In 42, the 4 is in the tens place and represents 40. The 2 is in the ones place and represents 2. The same digit can have different value in another position.
Numbers can be composed and decomposed
57 can be written as 5 tens and 7 ones, as 50+7, or with base-ten blocks. These representations describe the same number.
Zero can hold a place
In 60, the 6 means six tens and the 0 means zero ones. Zero shows that no extra ones remain beyond the complete tens.
Interactive math lab
Change it. See what stays true.
Base-Ten Lab
Change hundreds, tens, and ones and watch the total rebuild from place value.
- bundle ones
- build number
- read digit value
- expanded form
Worked examples
Twenty different ways to see the concept work.
23 as tens and ones.
2 tens, 3 ones20+3=23.
34 as tens and ones.
3 tens, 4 ones30+4=34.
45 as tens and ones.
4 tens, 5 ones40+5=45.
56 as tens and ones.
5 tens, 6 ones50+6=56.
67 as tens and ones.
6 tens, 7 ones60+7=67.
78 as tens and ones.
7 tens, 8 ones70+8=78.
89 as tens and ones.
8 tens, 9 ones80+9=89.
90 as tens and ones.
9 tens, 0 onesNo loose ones remain.
What value does 4 have in 47?
40Four tens equal forty.
What value does 7 have in 47?
7Seven ones equal seven.
Build 32.
3 tens + 2 ones30+2.
Build 71.
7 tens + 1 one70+1.
Expand 58.
50+8Five tens and eight ones.
Expand 40.
40+0Four tens and zero ones.
Which numeral is 6 tens 3 ones?
63Tens digit 6, ones digit 3.
Which numeral is 9 tens 2 ones?
9290+2.
Swap digits 24→42. Same value?
No2 tens 4 ones differs from 4 tens 2 ones.
Why is 52 greater than 25?
Five tens exceed two tensDigit position determines value.
Regroup 10 ones.
1 tenA base-ten unit is formed.
Explain 100 in tens.
10 tensTen groups of ten make one hundred.
Practice
Guided practice with hints
01Represent 36.
Hint: Group into tens first.
Answer: 3 tens 6 ones
02What does 5 mean in 54?
Hint: Look at its place.
Answer: 50
03What does 4 mean in 54?
Hint: Ones place.
Answer: 4
04Write 7 tens 2 ones.
Hint: Put 7 in tens, 2 in ones.
Answer: 72
05Expand 81.
Hint: Eight tens plus one.
Answer: 80+1
06Explain 30.
Hint: Complete tens with no loose ones.
Answer: 3 tens 0 ones
Practice
Independent practice
0124 in tens/ones
Answer: 2 tens 4 ones
0263 in tens/ones
Answer: 6 tens 3 ones
0390 in tens/ones
Answer: 9 tens 0 ones
045 tens 8 ones
Answer: 58
057 tens 0 ones
Answer: 70
06Expand 46
Answer: 40+6
07Value of 3 in 37
Answer: 30
08Value of 7 in 37
Answer: 7
Common mistakes
Learn to catch the error, not just the answer.
Use place position: a 4 in tens place means forty.
Zero records that there are no ones beyond five complete tens.
Compare base-ten models of 24 and 42 to see different numbers of tens.
Applications & challenge
Use the idea beyond a single exercise.
Applications
- Bundle sticks into tens and record the total with loose ones.
- Represent classroom quantities with base-ten blocks before writing numerals.
Challenge problems
Why is 68 not six plus eight?
The 6 represents six tens, or 60, so 68=60+8.
How many ones are equivalent to 7 tens?
70 ones
If 49 gains one, what place-value change occurs?
9 ones plus one become a new ten, making 5 tens 0 ones = 50.
Explain why 30+7 and 3 tens 7 ones are equivalent.
Three tens equal 30, and seven ones add 7; both represent 37.
Flashcards
Retrieve it from memory.
Flashcards
Card 1 of 6
Game mode
Build the Number
Construct a two-digit number with tens rods and ones, then write expanded and standard forms.
Practice
Mastery check
0135 in tens/ones
Answer: 3 tens 5 ones
0272 in tens/ones
Answer: 7 tens 2 ones
03Write 4 tens 6 ones
Answer: 46
04Expand 59
Answer: 50+9
05Value of 8 in 84
Answer: 80
06What is 10 ones?
Answer: 1 ten
07What does zero mean in 60?
Answer: There are no extra ones.
08Why does place matter?
Answer: Position determines the value represented by a digit.
Terminology
Words to know
- tens place
- The position showing how many groups of ten.
- ones place
- The position showing how many single units.
- expanded form
- A number written as the sum of its place values.
- regroup
- Exchange equivalent units, such as ten ones for one ten.
Continue learning
Connected concepts
Curriculum references
Standards and instructional references
California Common Core State Standards for Mathematics — Grade 1 Number & Operations in Base Ten
Grade 1 counting, place value, numeral representation, and comparison progression.