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.

Learning Targets (I can)

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.

About the Math

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)
partial sums
symbols (equations)
calculators

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. 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.

Decomposition of Numbers
Addition With A Number Chart
Addition On A Number Line
Addition: Partial Sums

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.

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 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.	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.

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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Preferred Resources

Preferred Tasks

These links are HCPSS created instructional tasks. These tasks are provided in Google slides. When selected, a copy of the file is added to your drive for classroom use.

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:

Sara's Sweet Shop
Sara's Sweet Shop Follow Up #1
Sara's Sweet Shop Follow Up #2

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:

Lesson Seeds (Prompts for Rigor)

Rigorous mathematics instruction balances the teaching and learning of conceptual understanding, procedural understanding, and the application of mathematics standards. Below are prompts for applying rigor in your classroom. They may support small group instruction or whole group collaborative investigations. They are intended to serve as a starting point for planning . See the Increasing Rigor page for more information.

Anna scored 18 points in 3 games. What might her scores have been for each of the games?
Juan added three numbers to get 14. What could the three numbers be?
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?

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Additional Resources

Additional Tasks and Lesson Seeds

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)
Job Chart (Utah Core Academy Lesson)
Month Page (Utah Core Academy Lesson)
Adding 10 at Disneyland (Utah Core Academy Lesson)

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.

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

Children's Literature Connections

Children’s Literature provides an opportunity to put mathematics in context. These titles connect well with this standard.

Fair Bear Share

by Stuart Murphy

Available on Amazon

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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)

online Practice

These links provide online resources to engage students during independent or center time.

Independent Practice

These resource sheets can be used for independent practice or homework. They are intended to reinforce procedures and concepts. They should not be used as a source of direct instruction or whole-group practice.

HOmEWoRK

These resource sheets can be used for independent practice or homework. 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

Learning Targets

K-2 rubric.jpg

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.

Learning targets identify what students should be able to do. The resources below can be used to measure student understanding of the standard. The rubric can be applied to any tasks and observations for assessment and/or grading.

Rubric for Tasks (pdf)

Assessment Tasks

These tasks align with the learning targets for the standard. They can be combined with other tasks for extended assessment opportunities. Teachers/students are not expected to complete all these tasks.

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