Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
10 can be thought of as a bundle of ten ones — called a “ten.”
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
Measurement Topic
This standard is reported on the report card in these quarters as follows:
1st Grade Students Learning 1st Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of number concepts and relationships.
Report Card Measurement Topic:Demonstrates understanding of number concepts and relationships.
Kindergarten Students Learning 1st Grade Standards
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Report Card Measurement Topic:Demonstrates understanding of number concepts and relationships.
About the Math
Skills and concepts below are learning goals for this standard.
The concept of ten is a foundational skill in primary mathematics. Students must be able to compose ten in order to add and subtract as well as understand the value of a number. Understanding the composition of a two-digit number is equally important. Students need ample practice so that understanding is intuitive rather than rote or memorized.
Represent 10 as ten ones.
Ten ones become a ten just as ten tens become a hundred and ten hundreds become a thousand. Students need ample practice bundling. Though this likely occurred in kindergarten, practice is likely needed in grade 1 as well. Using varied tools is important. Consider ten frames, beans on sticks, cm cubes in dixie cups, digi-blocks, and of course base ten blocks - knowing that they cannot be grouped but are instead exchanged. This can be problematic early in first grade.
Represent numbers 11 to 19 as a ten and some ones.
Students were exposed to this idea in kindergarten. This is the natural extension of the previous learning target. Once this is understood deeply students should transfer this idea to numbers 21-29, 31-39, and so on. Students should see that all of these are related.
Represent multiple sets of ten using physical tools, drawings, and number names (2 tens is 20).
Models support this learning target. Here, students should connect their representations to number charts and other tools. Number lines are appropriate later in grade 1. Students should work with pre-grouped models such as base ten blocks and ungrouped models such as digi-blocks or manipulative ten frames. Proportionate models (including those named) are also recommended. Disproportionate models can be used for extending student thinking. Virtual base ten blocksLinks to an external site. , Chip AbacusLinks to an external site., and hundred chartsLinks to an external site. are good electronic resources.
Explain the value of each digit in a two-digit number (place value).
Digits represent value. 93 represents 9 tens and 3 ones whereas 39 represents 3 tens and 9 ones. There is a considerable difference between the two. Moreover, these two are located at different places on a hundred chart, on number lines, and with different base ten models. Students need to understand that 37 can be named as 37 ones or grouped by tens to be 3 tens and 7 singles. So the way we say a number such as "thirty-seven" needs to be connected with the grouping by tens concept. There are several ways to use the base-ten language for a number such as 37. Thirty-seven can be 3 tens and 7; 3 tens and 7 ones; 3 groups of ten and 7 leftovers; 3 tens and 7 singles. All of these can be used to describe the meaning of "thirty-seven." If appropriate, this learning target can be extended to representing a number in multiple ways. For example, 37 can be shown as 3 tens and 7 ones or 2 tens and 17 ones, or simply 37 ones.
Locate a two-digit number on a hundred chart and number line.
As students develop an understanding of two-digit numbers through base ten models, we should begin to connect the understanding to hundred charts and number lines. Students should first work with ticked number lines and move to open number lines if understanding is evident. In grade 1, it is recommended to rely on hundred charts and ticked number lines.
Essential vocabulary for this standard includes place value, digit, value, hundred chart, number line, and group.
Progression of Standard within Grade 1
This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.
Progression Throughout Year
Quarter 1
Quarter 2
Quarter 3
Quarter 4
Represent 10 as ten ones.
Represent numbers 11 to 19 as a ten and some ones.
Represent multiple sets of ten using physical tools, drawings, and number names (2 tens is 20).
Explain the value of each digit in a two-digit number (place value).
Locate a two-digit number on a hundred chart and number line.
Represent 10 as ten ones.
Represent numbers 11 to 19 as a ten and some ones.
Represent multiple sets of ten using physical tools, drawings, and number names (2 tens is 20).
Explain the value of each digit in a two-digit number (place value).
Locate a two-digit number on a hundred chart and number line.
This includes representing 100 with a "flat" base ten block.
**Revisit this standard through routines, independent practice, discussions, and other activities.
**Revisit this standard through routines, independent practice, discussions, and other activities.
These tasks can be used with small group or whole group instruction.
You will need something you have many of : popsicle sticks or coffee stirrers and rubber bands. Put out some sticks on the table (any amount less than 60). Have the students predict how many sticks you put out. Ask what they think a good way to count them could be. Start counting them and when you reach 10, make a bundle of them to show that this is one group of ten. Have them help you continue to count and bundle when you get a group of ten. About halfway through counting have them look again at the bundles and leftovers and change their predictions. After you finish bundling all the tens have the students chorally count by 10s then 1s to check the total. Write the tens digit under the bundles and the ones digit under the leftover sticks. Ask could we switch the places of the digits? Why or Why not? Continue practicing all together estimating, then counting and bundling tens to help count for a few numbers. Then give each pair a pile of sticks to count and bundle together and have them write the total number for their sticks.
Have students look at bucket of linking cubes and predict how many they could grab with two hands. Let them each grab two handfuls and predict how many they grabbed. Have them count their cubes and write their total. Ask what would be an easier way for us to look at some one else's cubes and see their total? If they don't come up with it, lead them to connecting 10 cubes to make a ten as they count so they can see it as tens and ones. Have them combine their cubes with a neighbor to again count their totals (making a new ten as needed).
Give each student base ten rods and units ( more than 10 per student). Ask them to build the number 16. Look at how each student makes it. Have them look at one another's to compare each way. If everyone uses a rod and 6 units, ask them if they could make 16 in another way. Continue with various 2-digit numbers. After they make one way continue to ask if they can represent it another way. If they don't come up with it say "Is there another way you could make (number) by using less tens and more ones?" As they make new ways show each way using a number bond to show how they decomposed their number (43 = 40 + 3 or 43 = 30 + 13).
Bring in a jar of beans or centimeter cubes ( over 100 but less than 120) and have the students each predict how many are in the jar. Ask for an efficient way to count all the beans or cubes. Using dixie cups or small plastic cups have the students help group the beans into groups of tens until there is no more tens. When you count them all ask if there is another way to group them to make it easier to count them all (group the 10 tens into a hundred) Count by 10s as you dump the 10 small cups of ten into a larger plastic cup. Recount the beans by counting a hundred, tens, ones to see the total.
How many different ways can you represent 82 using tens and ones?
Does 4 tens and 8 ones have the same value as 3 tens and 18 ones? Explain your thinking.
Do 2 tens and 6 ones have the same value as 2 ones and 6 tens? Use models and/or hundreds chart to help explain your answer.
A two-digit number has more tens than ones. What could the number be? What is another possibility?
The sum of the digits of a two-digit number is12. Use a hundred chart, what could the number be? What is another possibility?
How are the numbers 30 and 35 alike? How are they different?
Kendra made a two-digit number with a 6 in the ones place. What possible numbers could she have made?
SLIDE-BASED TASKS
These links are HCPSS created instructional tasks. These tasks are provided in Google slides. These tasks should be used for inspiration and resources, but instruction should start with students having the opportunity to engage with the math first(often involving physical and/or visual models) followed by discussion and explicit instruction to ensure student understanding.
These publications have been provided for each school. They are typically stored in team closets or the media center. Check with your team leader if you cannot find them.
Print Resources
Book Thumbnail
Book Title
Grade
Pages
Teaching Student-Centered Mathematics
K-3
Ten and Some More, Activity 2.26, Page 55 Groups of Ten, Activity 5.2, Page 130
These resource sheets can be used for independent practice, homework, or assessment. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.
Understand that the two digits of a two-digit number represent amounts of tens and ones. Understand the following as special cases:
10 can be thought of as a bundle of ten ones — called a “ten.”
The numbers from 11 to 19 are composed of a ten and one, two, three, four, five, six, seven, eight, or nine ones.
The numbers 10, 20, 30, 40, 50, 60, 70, 80, 90 refer to one, two, three, four, five, six, seven, eight, or nine tens (and 0 ones).
Measurement Topic
The standard is reported on the report card through these measurement topics. Expand the measurement topic for a description of what students who meet expectation are able to do.
First Grade Students Learning First Grade Standards by Measurement Topic
Use the links below to access a task for this standard as well as student work samples that are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.