1.OA.C.5 - About the Math, Learning Targets, and Increasing Rigor

Standard

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

 

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.   Report Card Measurement Topic: Demonstrates understanding of subtraction.

Kindergarten Students Learning 1st Grade Standards

Quarter 1	Quarter 2	Quarter 3	Quarter 4
	Report Card Measurement Topic: Demonstrates understanding of addition.   Report Card Measurement Topic: Demonstrates understanding of subtraction.

 

About the Math

Skills and concepts below are learning goals for this standard.

• Represent addition and subtraction with base ten blocks, counters, ten frames, number lines, and drawings.
• Add by counting all and counting on.

As students use tools to show addition, they should be positioned to recognize that adding is counting all or counting on. The latter is especially useful for adding larger numbers. Either way, when one counts all or counts on (using the same quantities) the last number said/counted is the same. 

• Explain that one can count on from either addend in an addition equation.

This is essentially an application of the Commutative Property though formal introduction of the property is not warranted here. Students should investigate this learning target with all sorts of tools and representations and should be able to justify that it applies always. Students should also explain why it's better to start with certain addends. For example, with 2 + 9, it's more efficient to begin with 9 and count on 2.

• Recognize that +1 means the next number and that +2 means the next-next number in the counting sequence.

Students have been counting by 1 for some time. Students should also have practice counting by 2. Students should then connect this to adding 1 or adding 2. The work should be connected to the appropriate equation. This is also an early strategy for the +1/+2 basic fact set.

• Subtract by counting back or counting on.
• Explain that one can count back the total amount being subtracted (i.e. in 9-7, one can count back 7) or that one can count back to the number being subtracted (i.e. in 9-7, one can count back to 7).
• Recognize that -1 means the number before and that -2 means the number that is two numbers before in the counting sequence.

Similar to counting on one more and two more, we can count back by one and two. This is a good way to find the difference. It is helpful for developing understanding and recall. Students should also relate -1 or -2 situations to +1 and +2 situations (i.e. counting on). 

Students need to see that when they count 2 more or 2 less, they are actually adding 2 and taking away 2. At first, students may identify this with counting instead of the relationships between numbers. Eventually, we want students to see that 7 is two more than 5 and that 8 is two less than 10. Dot plates, calculators, part-part-whole models can all be used to represent these relationships.

Essential vocabulary for this standard includes: addition, subtraction, count on , and count back (online dictionary Links to an external site., HCPSS Vocabulary Cards Download HCPSS Vocabulary Cards

).

 

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 addition and subtraction with base ten blocks, counters, ten frames, number lines, and drawings. Add by counting all and counting on. Explain that one can count on from either addend in an addition equation. Recognize that +1 means the next number and that +2 means the next-next number in the counting sequence. Subtract by counting back or counting on. Explain that one can count back the total amount being subtracted (i.e. in 9-7, one can count back 7) or that one can count back to the number being subtracted (i.e. in 9-7, one can count back to 7). Recognize that -1 means the number before and that -2 means the number that is two numbers before in the counting sequence. (Associated with 1.OA.C.5, Q1)

 

Progression of this Standard Across Grades

This progression is informed by the Achieve the Core Coherence Map Links to an external site.. Information is not the complete standard.

Progression Across Grades

Kindergarten	Grade 2
Understand the relationship between numbers and quantities (K.CC.4)	Fluently add and subtract within 20 using mental strategies (2.OA.2)

 

 

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TASKS

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

• Give each group of students a different manipulative to work with (unifix cubes, counting bears, ten frames with counters, 1-20 number lines, etc.) Put an equation on the board such as 4 + 3 and have the students work together to model it with their manipulative. Have the students do a gallery walk to see all the different ways to represent the problem and then highlight a few ways. Rotate the materials so each group gets to try each manipulative for various addition equations. (3 +2, 7+ 3, 6 + 5). Debrief at the end what was their favorite way of representing addition and why. Repeat the same activity with subtraction equations. Discuss what is challenging about representing subtraction using manipulatives. 
• Give each pair of students a number cube and a stack of digit cards, and 10 counters or cubes. Have one partner draw a digit card while the other rolls the die. They build the number rolled using the cubes to help count on that many from the digit card number. Have them write the equation once they solve. (example: student pulls a 6 and their partner rolls a 3. They get out 3 cubes and count on from 6 to figure out what 6 + 3 more is and record their equation and answer). Have them repeat to continue practicing counting on to add. 
• Have the students sit in a circle. Have one student roll 2 10-sided dice to make a 2-digit number. Have students take turns counting on or counting back from that number until they make it around the circle. After it makes it all the way around the circle, have the students pass the dice to the person besides them and continue. After two times around the circle, have students make predictions about what number they will reach when they stop. Debrief about if they were close after counting around the circle and how they can make a better prediction for the next time around. (have a hundreds chart available to assist when needed)
• Have pairs of students roll two dice or draw two digit cards to make a 2-digit number. Have one student build the number that is 1 less and the other build the number that is one more using base ten blocks. Have them change rolls as they continue to practice. Continue on with building the number that is 2 less or 2 more once 1 less and 1 more becomes easy.
• When Austin solved his math problem on the number line, he was counting up. He started at a certain number, and he counted up 4 more. When he stopped, he was at a number greater than 20. What three different numbers could he have started at?
• How are addition and subtraction related?
• What strategy do you use when solving 34 + 2 = and 75 - 2 = ? Explain your thinking.

 

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.

 

Additional Tasks

  These links provide instructional ideas connected to this standard. [NOTE: NCTM membership required for access to Illuminations lessons.]

• The Very Hungry Caterpillar  Links to an external site. (Illustrative Math)
• Stairsteps One More, One Less Download Stairsteps One More, One Less
  (Utah Core Academy Lesson)
• Teddy In the Middle of the Line Download Teddy In the Middle of the Line
  (Utah Core Academy Lesson)
• Two Eyes Download Two Eyes
  (Utah Core Academy Lesson)
• Let's Go Skiing Download Let's Go Skiing
  (Utah Core Academy Lesson)
• Getting Ready to Play Download Getting Ready to Play
  (Utah Core Academy Lesson)
• The Very Hungry Caterpillar Links to an external site. (Achieve the Core Lesson)
• Frogs On a Logs Links to an external site. (NCTM Illuminations Lesson)
• Counting Back and Counting On Links to an external site. (NCTM Illuminations Lesson) Links to an external site.
• How Many More? Links to an external site. (NCTM Illuminations 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 Thumbnail	Book Title	Grade	Pages
	Teaching Student-Centered Mathematics	K-3	Real Counting On, Activity 2.7, Page 41 One/Two-More-Than Dice, Activity 4.1, Page 100 Lotto for +1/+2, Activity 4.3, Page 100
	Mastering Basic Facts: Addition and Subtraction	1-2	(31-50)
	Math Intervention: Building Number Power	K-2	(100-103)

 

 

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Centers

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

• Count on Four in a Row Download Count on Four in a Row
  (HCPSS-adapted resource)
• Count on It Download Count on It
  (HCPSS-adapted resource)
• Count on One Dice Download Count on One Dice
  (HCPSS-adapted resource)
• Scoops of Counters Download Scoops of Counters
  (HCPSS-adapted resource)
• Show me One More Download Show me One More
  ( 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.

• Count On or Count Back 1 or 2 a Links to an external site.
• Count On or Count Back 1 or 2 b Links to an external site.
• Apply ±1 and ±2 to Identify 1 or 2 More/Less than a Number A Links to an external site.
• Apply ±1 and ±2 to Identify 1 or 2 More/Less than a Number B Links to an external site.
• Count On/Count Back by 1 within 10 Links to an external site.
• Count On/Count Back by 1 within 20 Links to an external site.
• Playing Cards (Count On) Links to an external site.
• Count On/Count Back by 1 and 2 within 20 A Links to an external site.
• Count On/Count Back by 1 and 2 within 20 B Links to an external site.

 

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Full Standard

Relate counting to addition and subtraction (e.g., by counting on 2 to add 2).

 

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.

 

1st Grade Students Learning 1st Grade Standards by Measurement Topic

 

Kindergarten Students Learning 1st Grade Standards by Measurement Topic

 

1OA5 Anecdotal Data Collection Tool for Addition Links to an external site.

1OA5 Anecdotal Data Collection Tool for Subtraction Links to an external site.

 

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) Links to an external site.

 

Exemplars for this standard

Use the links below to access 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.

Playing Cards

• Printable Task Links to an external site.
• Student Exemplars Links to an external site.

 

 

 

 

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