Grade 1 Number Operations

1.NBT.C.4

About the Math

Full Standard

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

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 addition.

**Kindergarten Students Learning 1st Grade Standards**
Quarter 1	Quarter 2	Quarter 3	Quarter 4
			Report Card Measurement Topic: Demonstrates understanding of addition.

About the Math

Skills and concepts below are learning goals for this standard.

Explain addition within 100 adding a two-digit number and a one-digit number using physical models, drawings, hundred charts, and number lines.
Explain addition within 100 adding a two-digit number and a multiple of ten number using physical models, drawings, hundred charts, and number lines.
Explain addition within 100 adding a two-digit number and a two-digit number using physical models, drawings, hundred charts, and number lines.
Use partial sums by decomposing both addends to add within 100. (Partial Sums Parent Brief)
Use counting on by decomposing one addend to add within 100. (Count On Parent Brief)
Explain why a new ten is sometimes made when adding numbers. (Make Ten Parent Brief)

There are many ways to add numbers within 100. Sometimes, we might decompose one or both addends. Sometimes, we might count on by ones (38 + 4) from a number and other times we might count on by groups of 10 (38 + 40).

Students should work with various models and representations to develop understanding of the mathematics. Models, tools, and representations that students should use include:

base ten blocks (physical or drawing)
ten frames
hundred charts
number lines (open/empty and closed)
symbols (equations)

There is no specific progression of representations. Instead, students should connect understanding from one representation to the next. Physical models and drawings should be connected to addition on number charts/number lines, and equations. Not all representations are helpful with all strategies. For example, partial sums shown on a 120 chart is generally not helpful. Be thoughtful about which representation(s) makes the most sense and connect to equations. Regardless of the representation being used by students, teachers should connect representations to a symbolic recording (equation). First graders should not be exposed to or taught the traditional algorithm for addition.

Estimation and Number Lines: We can have students estimate sums prior to finding sums to develop their sense of reasonableness of answers. Students must understand number lines and work with "ticked" number lines before moving to open number lines for adding. Essential vocabulary for this standard includes(online dictionary, HCPSS Vocabulary Cards):

add,
compose,
decompose,
place value

Progression and Regrouping Notes: This standard should be developed as outlined below. First, students should work with addition of two-digit and one-digit addends. Then, they should add multiples of 10 to two-digit numbers. Lastly, students should work with adding two, two-digit numbers. NOTE: Addition situations should not be separated by the need to regroup. That is, students should not work with non-regrouping problems for a time and then work with regrouping problems. This reinforces misconceptions of different reasons and ways to add numbers.

Math In Minutes: The video links below demonstrate strategies for addition.

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
		Explain addition within 100 adding a two-digit number and a one-digit number using physical models, drawings, hundred charts, and number lines.	Explain addition within 100 adding a two-digit number and a one-digit number using physical models, drawings, hundred charts, and number lines. Explain addition within 100 adding a two-digit number and a multiple of ten number using physical models, drawings, hundred charts, and number lines. Explain addition within 100 adding a two-digit number and a two-digit number using physical models, drawings, hundred charts, and number lines. Use partial sums by decomposing both addends to add within 100. Use partial sums by decomposing one addend to add within 100. Explain why a new ten is sometimes made when adding numbers.

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map. Information is not the complete standard.

Progression Across Grades
Kindergarten	Grade 2
Compose and decompose numbers from 11 to 19 into ten ones and some ones (K.NBT.1)	Fluently add and subtract within 100. ( 2.NBT.5 ) Use addition and subtraction to solve one- and two-step word problems (2.OA.1)

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Instructional Tasks

TASKS

These tasks can be used with small group or whole group instruction.

Print a tens and ones place value chart for each student to use with their base ten blocks. Show the problem 23 + 4 and ask the students how would they solve it. Let them solve and walk around to see their strategies. Debrief and have several students share their strategies. Did everyone get the same sum? Pose another problem such as 41 + 5 and let the students solve in anyway they choose. Observe to see if more students might be combining the ones and using place value strategies rather than counting strategies. (know they can just add 5 and 1 and then the 4 tens instead of counting all together. Now try one that gets 10 ones like 34 + 6. Let the students solve and ask what the sum is. What is another way we could show the sum besides 3 tens and 10 ones. Could we trade in the ones for a ten? Point out when they fill the ten frame they make a new ten with ones and can regroup it for a ten rod so the answer is easier to see. Continue practicing with problems like 27 + 5 by having them fill in the tens frame knowing when and how many to regroup as needed.
Put up the problem 45 + 5. Ask how we can show the number 45 as tens and ones. Show it decomposed. Ask How could we solve the problem 40 + 5 + 5. See what the students share. Hopefully they will see 45 + 5 is the same problem as 40 + 10 to get the answer. Try another one like 36 + 6. Decompose 36 and see what the students suggest. Some may be able to double 6 to get 12 but then do not know what to do with 30 + 12. You can also remind them we want to try to make a new ten to help us add to help lead them to 30 + 6 + 4+2 by decomposing the addend 6 to 4 and 2 to help make a new ten from 36. Be sure to make an anchor chart to show how to use models and partial sums when adding a two-digit number to a single digit.
Use tens and ones place value chart and base ten blocks for each student. Put up the problem 46 + 20 on the board and ask for students to share ideas on how to solve this problem. Ask them to build 46 on their place value mats and then tell them we are going to add 20 more. Walk around and look at their strategies. Ask as you debrief what the sum is and how they know. Ask did you count them all? Did someone do it a different way? Then give another problem such as 64 + 30. Have them share out their strategies as they are finished. Then pose the problem 40 + 17. While debriefing ask again for strategies. If no one shares switching the order ask: would it be easier to count on if we started with 17? Can we switch the order of the addends? If they are unsure show how to start with 17 and count on 4 tens to see the total. Continue practice until you are ready to debrief. Gather them to look at all the equations. What do you notice? Did the ones place change? Did the tens place change? What's something we notice when we are adding tens? Repeat this same activity for adding 2 two-digit numbers by building one number and then adding on the tens and then the ones to find the total to practice counting on.
Gather the students up front. On the board write the equation 35 + 20 next to an open number line. Ask how could we solve this equation on a number line? Ask where should we put 35 on the number line? Why? Put 35 at the beginning of the number line and tell them to turn and talk about how we could add on 20 more. What should we jump by? Have someone come up and draw the first hop of 10. What number do we land on? Why is important to show where you land on an open number line? Are we done solving? How many more hops of 10 do we need to do? How do you know? Have someone else come up and show the next hop of 10. How do we know we are done? Ask do you think there is a different way to solve 35 + 20 on a number line? Say you have seen a student start at 20. Ask if I start with 20 how many will I need to count on? Show 3 hops of 10s having them tell you the landing numbers. Am I done? What else do I need to hop? Show the hop of 5 and where you landed. Did we solve the same problem? Is it okay to do it this way? Have them work with partners at their seat practicing solving equations of adding tens to a two digit number using a number line. Repeat this same type of activity when adding 2 two-digit numbers by hoping by 10s and then counting on by ones on open number lines.
The sum of a two-digit number and a one digit number is 43? What might the numbers be?
Have students randomly pick a two-digit number from the hundred chart. Then roll a ten-sided die to find a digit to add to the number. What strategies are you using when you are adding? For example, in 48 + 7 = , students might say “I broke the 7 into 2 and 5 because I know 8 + 2 is 10 and so 48 and 2 is 50 and 5 more is 55?
Create some number sentences with the students and record three on the board. For example, 38 + 10 = 48, 24 + 30 = 54, 57 + 40 = 97. Ask "What patterns do you see?"
Use a 100 chart. Choose two numbers between 11 and 50 to add. Show how to use the chart to add the numbers without using pencil or paper.
Use six of the digits 1-9 (without repeating digits) to form 2 two-digit numbers with a two-digit sum that is true. (for example: 64 + 15 = 79) Can you think of another example?
Two two-digit numbers have a sum of 86. What could the addends be? What is another solution?
Start with the number 15, then have students reach into a bowl of tens and ones block and grab a handful of blocks to form a number. Add 15 to the other number. Compare your addition sentence to your neighbor’s addition sentence, how are they alike and how are they different?

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.

Module 12 • Multi-Digit Addition

Represent addition of two-digit addend + one-digit addend with models connected to hundred charts and number lines:

Represent addition of two-digit addend + multiple of ten addend with models connected to hundred charts and number lines:

Represent addition of two-digit addend + two-digit addend with models connected to hundred charts and number lines:

Colorful Crayons (decomposing both addends)
Colorful Crayons Follow Up (decomposing both addends)
Sweet Treats Candy Shoppe (decomposing only one addend)
Sweet Treats Candy Shoppe Follow Up (decomposing only one addend)
Adding Counting Collections

Add two, two-digit numbers:

Additional Tasks

These links provide instructional ideas connected to this standard.

Graham Cracker (3 Act Task, G.Fletcher)
Bright Idea (3 Act Task, G.Fletcher)
Pick A Card (Utah Core Academy Lesson)
Adding 10 at Disneyland (Utah Core Academy Lesson)

Tasks From Print Resources

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 Title	Grade	Pages
Teaching Student-Centered Mathematics	K-3	Ten-Frame Adding and Subtracting, Activity 6.1, Page 165
Number Talks	K-5	various
Brain Compatible Activities for Mathematics	K-1	(36-39, 57-59)
Mental Math in the Primary Grades	K-2	(66-76)
Math In Practice Teaching First-Grade Math	1	Module 8

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Independent Work

Centers

These print resources can be used during independent or center time. These resources could also be used as lesson seeds.

Adding Longs (HCPSS-adapted resource)
How Many Ways (HCPSS-adapted resource)
Jump Back by Ten (HCPSS-adapted resource)
Lucky Sums (HCPSS-adapted resource)
Two Digit Plus One Digit Adding (HCPSS-adapted resource)
What Goes There? (HCPSS-adapted resource)

Independent Practice/Homework/Assessment

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.

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Assessment

Full Standard

Add within 100, including adding a two-digit number and a one-digit number, and adding a two-digit number and a multiple of 10, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used. Understand that in adding two-digit numbers, one adds tens and tens, ones and ones; and sometimes it is necessary to compose a ten.

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

Demonstrates understanding of addition

Quarter 4

Model addition within 100 adding a two-digit number and a one-digit number using physical models, drawings, charts, number lines, and equations.
Model addition within 100 adding a two-digit number and a multiple of ten using physical models, drawings, charts, number lines, and equations.
Model addition within 100 adding a two-digit number and another two-digit number using physical models, drawings, charts, number lines, and equations.
Use partial sums and count on strategies to add.
Explain strategies used to add using place value understanding.

Kindergarten Students Learning 1st Grade Standards by Measurement Topic

Demonstrates understanding of addition

Quarter 4

Model addition within 100 adding a two-digit number and a one-digit number using physical models, drawings, charts, number lines, and equations.
Model addition within 100 adding a two-digit number and a multiple of ten using physical models, drawings, charts, number lines, and equations.
Model addition within 100 adding a two-digit number and another two-digit number using physical models, drawings, charts, number lines, and equations.
Use partial sums and count on strategies to add.
Explain strategies used to add using place value understanding.

1NBT4 Anecdotal Data Collection Tool

Visit the SBIR (Standards Based Instruction and Reporting) page in Course Essentials for more information and clarification.

Rubric (for thinking and reasoning evidence)

Use this rubric for observation and constructed responses (tasks that require explanation, justification, and/or representation).

Rubric for Tasks (pdf)

Exemplars for this standard (if available)

These samples are examples of what it might look like for a student who MEETS EXPECTATIONS, is MAKING PROGRESS, and/or is MAKING LIMITED/NO PROGRESS.

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