2.OA.C.4 - About the Math, Learning Targets, and Increasing Rigor

Full Standard

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

Measurement Topic

This standard is reported on the report card in these quarters as follows:

About the Math

Skills and concepts below are learning goals for this standard.

• Use addition to find the total number of objects in an array.

An array is an arrangement of objects in rows and columns. Each row has the same number of objects in it. One can repeatedly add the values in an array to find the total. At this point, there is no need to connect an array or the act of finding the total number of objects to multiplication.

• Represent the total number of objects arranged in a rectangular array as an expression with the repeated addition of number of objects in each row (or column). For example if there are 3 rows with 4 objects in each row, I can write the expression 4 + 4 + 4 or I can write 3 + 3 + 3 + 3.
• Write an addition equation (e.g., 3 + 3 + 3 = 9) to express the total as a sum of equal addends.

The image to the right can be represented as 3 + 3 + 3 + 3 = 12 or 4 + 4 + 4 = 12. Both are correct. Students should be able to connect their equations directly to the array they are citing.

Essential vocabulary for this standard includes: rectangular array, addends, row, column, repeated addition, and equal groups. 

Progression of Standard within Grade 2

This progression informs how to develop the standard within the grade level. This progression is provided by HCPSS Elementary Mathematics.

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.

TASKS

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

• Distribute a bag of digit cards with the digits 1-5 in them and a bag of red/yellow counters. Pair students and have one student pick one card and make that many rows. The other student will pick another digit card and build that many columns. Have the pair build the rest of the array, if needed.  Then have the pair record the addition equation.  For example, if if the first partner draws a 3, they represent three rows. If the second partner draws a 2, they use the counters to make that many columns. Then they could write to make the addition equation 2 + 2 + 2 = 6 or 3 + 3 = 6.  Ask questions such as what do you notice about the number of counters in the first row? What do you notice about the number of counters in the second row? What do you notice about the addends? What does the sum tell you about your model?
• Distribute12 square tiles and grid paper to each group. Have them make as many arrays using all 12 tiles, record the array by coloring it on the grid paper and write the repeated addition equation next to the model. As students are able to discover all of the arrays for 12 tiles, be prepared to give them additional tiles and paper. Tiles that total 16, 18, and 24 are powerful numbers for students to use to explore arrays. As they explore, use phrases such as groups of, rows of, and pairs of. 
• Using a skip counting number routine while teaching this standard will help students make connections between rows, columns, and the total.
• There are some flowers in a vase. Each flower has equal amounts of petals. How many flowers are in the vase? How many petals are there? Draw an array and repeated addition sentence to show your work.
• Take a handful of square tiles. Can you make an array? Why or why not? If not, how can you make it an array? After you make your array, write a repeated addition sentence to express the total number of square tiles.
• Using 16 objects, make an array with equal rows and columns. Write a repeated addition sentence to represent this array. Can you make a different array with the 16 objects? What would be the number sentence for your new array? How are the number sentences similar? (equal addends) *this might take students past the 5 rows/5 columns, but is good enrichment*
• How does using an array help you count quicker?
• How would you explain to a friend how to best count an array? Is there a number sentence that can match how you count?
• Draw an array that has a total less than 12. If you add more columns would your array look like a train or tower?

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. 

• Cover the Floor Links to an external site. (3 Act Task, G.Fletcher)
• Counting Dots in Arrays Links to an external site. (Illustrative Math)
• Delayed Gratification Links to an external site. (Illustrative Math)
• Tri-Triangles Links to an external site. (Inside Mathematics Performance Task)
• Missing Lockers Download Missing Lockers
  (Utah Core Academy Lesson)
• Zoo Arrays Download Zoo Arrays
  (Utah Core Academy Lesson)
• Array Garden Task Download Array Garden Task
  (Utah Core Academy Lesson)
• Farmer Brown's Orchard Download Farmer Brown's Orchard
  (Utah Core Academy Lesson)
• Angela's Equal Groups Download Angela's Equal Groups
  (Utah Core Academy Lesson)
• Classroom Seating Chart Download Classroom Seating Chart
  (Utah Core Academy Lesson)
• Cookie Monster, Pg. 39 Links to an external site. (Georgia Department of Education 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	83 (Finding Factors, Activity 3.4)
	Hands-On Standards	1-2	52-53 (Decomposing Numbers) 54-55 (Repeated Addition)
	Brain-Compatible Activities for Mathematics	2-3	40-43
	Road to Reasoning	2	22-23 (Decorating Cupcakes) 68 (How Much Change?) 52 (Lights Out!)
	Math In Practice Teaching Second-Grade Math	2	Module 3

Centers

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

• How Many Arrays Can You Make? Download How Many Arrays Can You Make?
   (HCPSS-adapted resource)
• Spin an Array Download Spin an Array
  (HCPSS-adapted resource)
• Various Squares Download Various Squares
  (HCPSS-adapted resource)
• Repeated Addition Game Download Repeated Addition Game
  (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.

• Use Addition to Find the Total in an Array a Links to an external site.
• Use Addition to Find the Total in an Array b Links to an external site.
• Match Expressions to Arrays (performance task) Links to an external site.
• Write Equations to Match Arrays Links to an external site.
• Draw Arrays and Write Equations Links to an external site.
• Using Addition to Find the Total in An Array Links to an external site.

Full Standard

Use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends.

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.

2nd Grade Students Learning 2nd Grade Standards by Measurement Topic

1st Grade Students Learning 2nd Grade Standards by Measurement Topic

2OA4 Anecdotal Data Collection Tool 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 (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.