Unit 1.3: Addition within 20

Different situations suggest different addition strategies, such as counting on, thinking about doubles, or making a ten. Different situations can result in the same sum. The expressions that represent situations with the same sum are equal. This relationship can be recorded with an equal sign.

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Unless otherwise noted, SFUSD Math Core Curriculum is licensed under the Creative Commons Attribution 4.0 International License

Teacher-facing pages are green

Student-facing pages are white

notes for teachers are in the speaker notes

New Learning:

Re-engagement:

• In Unit 1.1, students found number combinations to make 10 with two and three addends.

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• Students use various strategies and representations to solve Add To: Results Unknown and Put Together/Take Apart: Total Unknown word problems.
• Students understand the meaning of the equal symbol.
• Students understand the Commutative Property of Addition through exploration of changing the order of the addends.
• Students are introduced to the tape diagram through a number bond representation.
• Students build addition fluency through exploration of plus zero, plus one, plus two, make 10, doubles, and double plus one strategies.

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Suggested Lesson Sequence

Week 1: Sept. 28-Oct. 2

Students connect adding 0, 1, and 2 to counting on with a number line. They investigate the commutative property by changing the order of the addends to make the counting on easier.

Lesson 1: LS 1 Entry Task & Day 1 Seesaw Counting On

Lesson 2: LS 1 Day 2 & 3 Seesaw - Seagulls Story

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Week 2: Oct.5 - 9

Students investigate and use the doubles and doubles +1 addition strategies as they work toward fluency in addition.

Lesson 3: LS 2 Double Scavenger Hunt Seesaw

Lesson 4: LS 2 Day 1 Doubles Seesaw

Lesson 5: LS 2 Day 2 & 3 Doubles +0, +1, +2 Seesaw

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Week 3: Oct. 13-16

Lesson 6: LS 3 Day 1 - Seesaw 1.3 Lesson 6

Lesson 7: LS 3 Day 3 Seesaw L7- Addition Strategies on the Number Line

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Week 4: Oct. 19-23

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Lesson 8: Re-engagement Revisit any of the lessons or concepts that students may need before the Milestone Task.

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Milestone Task - 3-Read (IDA) Seesaw 1.3 Milestone Task (Spanish), (Chinese)

Chinese Milestone Slidedeck

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Synchronous and Asynchronous Teaching Options:

Synchro-

nous (live)

Asynchronous (time-delayed)

Technology Resources

• Ten Frame Sums to 10 or 20 - Fluency practice for addition

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• These Doubles Cards from I See Maths can be used as visual supports for students to make sense of and practice doubles within 10 and within 20.

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• The Bordering 10 cards from I See Maths help students to see how single-digit numbers are broken down for addition calculations that border (or cross) 10.

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• The Counting On Games from I See Maths help students learn to count on mentally

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• Addition Blocks is an interactive game with options for multiple speeds and difficulties that gives students practice with single digit addition fluency. The browser version is free.

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• Learn and explore sums to 20 and patterns on this Interactive Addition Chart

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• The Math Balance from Didax allows students to create equations and inequalities like 9 + 3 = 8 + 4 with a visual / kinesthetic element.

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Student PDFs

1.3 Classwork .S. .C.

1.3 Homework .S. .C.

New Routine: Data Routine

Objective: The Data Routine has both social and a math objectives:

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Social

• Students build community by sharing about themselves - their person, lives, interests, & preferences - learning about their classmate’s, finding and celebrating their similarities and differences
• Students build community by recognizing their shared environment (e.g. weather)

Math

• Students develop their understanding of categorical and measurement data (see progression of standards in the following slides and here) as they:
• Formulate questions
• Collect data
• Organize and display the data
• Analyze the data, and
• Interpret the results
• Students apply other important math ideas from all domains

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See the Data Routine slides for a description of how to incorporate this routine into your lessons.

Daily Routine: Number of Days in School

Objective: To build one-to-one correspondence, lay the foundation for an understanding of place value, and give students a concrete sense of the magnitude of numbers up to 180 and their relationship to the passage of time.

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See the Number of Days in School (Spanish) slides for a description of how to incorporate this routine into your lessons.

Daily Routine: Counting Routine

Objective: To provide students opportunities to count forward and backwards by various whole numbers and decimals, developing an understanding of patterns in counting, addition and subtraction (and later multiplication) and place value.

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See the Counting Routine slides for a description of how to incorporate this routine into your lessons.

Math Talks:Number Lines

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Objective: Students develop deeper number sense and estimation skills by determining whether a number is closer to 0 or closer to 10 using a number line.

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Description: These Math Talks are designed to encourage students to apply their knowledge of the number sequence, think about the relative distances between numbers, and strengthen their ability to anchor numbers to 0, 5, and 10.

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Question:

Where should ___ be on the number line? Is __ closer to 0 or 10? How do you know?

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Where should the target number be on the number line?

Will it be __ closer to 0 or 10? Why?

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I think it belongs_____.

I think it’s closer to ___ because_____.

Number Line Math Talk

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Where should the target numbers be on the number line?

Will they be close to each other or far apart? Why?

I think they belong______ .

The numbers are close/not close to each other because_____.

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What is the same and what is different about the two numbers?

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2

Number Line Math Talk

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Where should the target number be on the number line?

Will it be __ closer to 0 or 10? Why?

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I think it belongs_____.

I think it’s closer to ___ because_____.

Number Line Math Talk

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Where should the target numbers be on the number line?

Will they be close to each other or far apart? Why?

I think they belong______ .

The numbers are close/not close to each other because_____.

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What is the same and what is different about the two numbers?

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Number Line Math Talk

Lesson 1:LS 1 Day 1

Whole Class or Groups: Launch

• Share a story situation about Seagulls at the beach.
• Notice and Wonder when you add 0, 1, and 2.
• Introduce the number line.

Independent work: Explore Seesaw Counting On

• Circle the number in the box on the number line
• Spin the spinner (return to Seesaw)
• Add that number on the number line
• Write an equation to match

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• Students add 0, 1, and 2 to a given number.

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Whole Class or Groups: Summarize

• Demonstrate using counters on the number line with expressions
• Noticed patterns when they add 0, 1, and 2. Students may notice that the number doesn’t change when they add 0, that the sum is the next number on the number line when they add 1, or that they move over 2 numbers when they add 2. Core Math to Emphasize: Adding small quantities can be done by counting on. Counting on can be demonstrated on a number line.

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Math Norms

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Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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15 + 2 =

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15 + 1 =

15 + 0 =

Notice and Wonder

15 + 0 = 15

15 + 2 = 17

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15 + 1 = 16

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11 + 0 = ?

11 + 1 = ?

11 + 2 = ?

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Counting On

Lesson 2: LS 1 Day 2 & 3

Whole Class or Groups: Launch:

• Ask students what would happen if they started with the spinner number first and then added the card. Would the sum be the same or different?
• Play a couple of rounds and talk about which was easier? Counting on from the Number card (like Lesson 1 Seesaw), or counting on from the spinner?

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Independent work: Seesaw - Seagulls Story

• Students will use what they know about counting on to solve another story problem about the seagulls at the beach.
• How many brown? How many white?
• Can you draw a picture? Which number will you represent first?
• Where is ___ on your number line? Where is ___ in your picture?

• Students repeat Day 1, but in reverse order: spin spinner first, then add the number card.
• Students use what they know about counting on to solve another story problem about the seagulls at the beach.

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Whole Class or Groups: Summarize:

• Share student or given work samples- What’s the same? What’s different?
• Addition Strategies anchor chart.

Core Math to Emphasize: Changing the order of the addends (commutative property) can be used to make counting on easier. The number line can be used to demonstrate it.

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Math Norms

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Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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The same or different?

2 + 9 = 11 9 + 2 = 11

Counting On

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2 of the seagulls were brown and 6 were white.

2 of the seagulls were brown and 6 were white.

How many brown and white seagulls are there?

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• Show how you know with a drawing.
• Represent it on the number line.

2 of the seagulls were brown and 6 were white.

How many brown and white seagulls are there?

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2 + 6 = 8

2 of the seagulls were brown and 6 were white.

How many brown and white seagulls are there?

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6 + 2 = 8

What’s the same? What’s different?

2 + 6 = 8

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6 + 2 = 8

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Addition Strategies

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Lesson 3: LS 2 Day 1

Whole Class or Groups: Launch

• Doubles Song
• Where is the double in this picture?
• How many are in each half?

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Independent work: Explore Doubles Scavenger Hunt Seesaw

• Doubles Scavenger Hunt
• Students upload pictures or videos to Seesaw

Explore the concept that when something has two sets, we call it a double. Student find real world examples from their life.

Whole Class or Groups: Summarize

• Share student photos or videos and discuss.
• I think it’s a double because _______.
• There are _____ in each half.

Core Math to Emphasize: Doubles tend to be more easily learned addition combinations, the recognition of which can help build procedural fluency. Doubles addition can be represented with a tape diagram.

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Math Norms

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Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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Doubles Song

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Where is the double in this picture?

How many are in each half?

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Where is the double in this picture?

How many are in each half?

Doubles Scavenger Hunt...

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Look for things in your house or neighborhood that are doubles.

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• I think it’s a double because _______.

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• There are _____ in each half.

6 6

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Lesson 4: LS 2 Day 1

Whole Class or Groups: Launch

• Doubles Song
• Review previous lesson summary of the cubes and doubles
• Relate to number bond and tape diagram visual representations

Independent work: Explore Doubles Seesaw

• Review Seesaw assignment sample
• Students build a doubles number with the blocks and
• Record on the number bond and tape diagram.

Students explore doubles with linking cubes and see the relationship between a number bond and a tape diagram.

Whole Class or Groups: Summarize

• Screen shot student work from Seesaw, or annotate on the slides provided
• Make a list of doubles and notice patterns

Core Math to Emphasize: Doubles tend to be more easily learned addition combinations, the recognition of which can help build procedural fluency. Doubles addition can be represented with a tape diagram.

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Math Norms

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Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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6 6

6 + 6 = 12

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12

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12

6

6

6 + 6 = 12

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Seesaw Doubles

Build

Record on Number Bond

Record on Tape Diagram

What’s the same? What’s different?

Doubles

What patterns do you notice?

Lesson 5: LS 2 Day 2 & 3

Whole Class or Groups: Launch:

• Notice and Wonder - Doubles +0, +1, and + 2
• Build double 6s plus 1 with cubes. What happens when we add 1? would happen if we added 0? What would happen if we added 2?
• Relate to the tape diagram - What’s the same? What’s different?

Independent work: Explore: Doubles +0, +1, +2 Seesaw

• Pick a number to double
• Spin the spinner
• Add that number to the 2nd double
• Record expression and sum in the tape diagram
• Repeat for each number

• Students solve doubles +0, +1, and +2 problems with linking cubes and record them with a drawing or tape diagram.

Whole Class or Groups: Summarize:

• Addition Strategies anchor chart
• Notice adding 2 results in the next doubles pair

Core Math to Emphasize: Counting on can be combined with recognizing doubles to solve doubles +1 and doubles + 2 situations. These relationships can be represented with a tape diagram.

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Math Norms

52

Errors are gifts that promote discussion.

Answers are important, but they are not the math.

Talk about each other’s thinking.

Ask questions until ideas make sense.

Use multiple strategies and multiple representations.

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SAN FRANCISCO UNIFIED SCHOOL DISTRICT

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Notice and Wonder

6 + 6 + 0 = 12

6 + 6 + 2 = 14

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6 + 6 + 1 = 13

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6 6

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6 6 + 1

13

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13

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6 + 1

What’s the same? What’s different?

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__+__

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3+2

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What do you notice about adding 2?

Lesson 6: LS 3 Day 1

Whole Class or Groups: Launch: Math Talk - How many dots do you see? How do you see them?

• Record different student strategies.
• If no students moved dots to make a 10, demonstrate.
• Show making a 10 on a Number Bond.

Independent work: Explore:

Seesaw 1.3 Lesson 6 - 1. Use the number cards and the dots to fill the 10 Frames. 2. Find the sum and record your equation. 3. Use the microphone to record your strategy.

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• Add two numbers together and think about how the make a ten strategy might help them.

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Whole Class or Groups: Summarize Have two to three students show how they broke apart one of their numbers to make a ten. Record the way they broke apart their number and created a new 10 on the Double 10 Frame and the Number Bond. Highlight Making a 10 strategy on the anchor chart.

Core Math to Emphasize: When adding two numbers creates a sum greater than ten, it is possible to decompose one of the numbers to change the problem into 10 and some more. A ten frame can be used to demonstrate the process.

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Math Talk

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___ + ___ + ___ = ___

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___ + ___ + ___ = ___

• Can you make a ten? How?
• What is your equation now?

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___ + ___ + ___ = ___

Addition Strategies

Lesson 7: LS 3 Day 3

Whole Class or Groups: Launch: Notice and Wonder

• Decompose a 6 into 5 and 1, add 1 to make a 10, add 10 and 5
• Remind students of the work they did with counters and double ten frames to use the make a ten strategy to add.
• Highlight the addition strategies on the number line.

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Independent work: Explore: Number Lines 0 to 20 BLM

Seesaw L7- Addition Strategies on the Number Line

Drag the circles and arrows on the number line to solve the expression.

Write the equations that show your addition strategy.

Students use a number line to add numbers using the make a ten strategy.

Whole Class or Groups: Summarize

True or False ? Expressions with equal sums are equal. Decomposing a number to make a ten can make the equality more easily visible.

Core Math to Emphasize: A number line can be used to move from counting all toward a more fluent process when using the decomposing to make a ten strategy. Independent work: Equal - Not Equal Student .S. .C.

Notice and Wonder...

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6 + 9 =

+1 +5

9 + 6 =

9 + 1 = 10

10 + 5 = 15

Change the order

Make a 10

• Which number will you represent first?
• How many more will you need to make 10?
• How many will be left after that?

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True or False?

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9 + 4 = 6 + 7

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True or False?

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6 + 8 = 7 + 9

Fall District Assessment Milestone Task Overview

SFUSD uses the District Assessments to support the continuous improvement work of the district. Reading Inventory (RI) is the District Assessment for reading, and two specific Math Milestone Tasks are the District Assessments for math. Aggregate student results are summarized to inform district planning and programs. Teachers use individual results to inform instruction. An individualized Student Report is uploaded to ParentVUE for families.

Ideally, assessments will encourage students to reflect on what they have learned, rather than to focus on scores, and the District Assessment is no exception. In keeping with the Graduate Profile, students are part of a community of learners who work toward graduating as critical, collaborative thinkers using multiple resources. This assessment is intended to be administered and scored as you would any other Milestone Task, after unit instruction is complete, and not treated as a high stakes assessment. The assessment should not alienate students, shift the focus away from learning towards a grade, or lead to racialized outcomes. You may administer the task whole class, in small groups, or a combination of both; in-person, online, synchronously or asynchronously.

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District Assessment Milestone Task Guidance for Teachers

Milestone Task

Whole Class or Groups: Launch Synchronously with 3-Read Protocol

• Tell students that they will be showing you what they have learned about different addition strategies.
• They will show their work with math drawings used throughout the unit (Objects, Number Lines, Tape Diagrams, Ten Frames …)

Independent work: Seesaw Milestone, On the Farm (Chinese)

On the Farm BLM .S. .C., On the Farm Three Read BLM .S. .C. Number Lines 0 to 20 BLM, Ten and Double Ten Frames BLM

• This Milestone has 2 Parts
• Ask students to explain their work after they have finished. These strategies cannot always be seen on paper. Seesaw Milestone.

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• Students choose an addition strategy to solve an addition word problem and some equations.
• This task is the Fall SFUSD Math District Assessment.

Whole Class or Groups: On the Farm Rubric Teacher, Suggested Answer Guide

Core Math to Emphasize: The situation will determine the best strategy to use for adding two numbers. Strategies to consider are counting on, using doubles, or decomposing to make a 10. Student Work Samples and Commentary for paper version are available.

Notice and Wonder...

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What is this story about?

1st Read

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What are the quantities in the situation?

2nd Read

On the Farm

Farmer Sue collects the eggs that her chickens lay. She collected 8 eggs on Thursday and 7 eggs on Friday.

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How many eggs did she

collect altogether?

On the Farm

Farmer Sue collects the eggs that her chickens lay. She collected 8 eggs on Thursday and 7 eggs on Friday.

Show your thinking with a math drawing and an equation.

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Part 1

1 + 8 =

Show how you know.

8 + 5 =

Show how you know.

Part 2

On the Farm

Look for student’s current understanding of the core math: The situation will determine the best strategy to use for adding two numbers. Strategies to consider are counting on, using doubles, or decomposing to make a 10.

Use the Milestone task as formative assessment to determine potential areas for re-engagement during the next unit. On the Farm Rubric Teacher, Suggested Answer Guide, Student Work Samples and Commentary for paper version.

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Fall District Assessment Milestone Task Guidance

Fall District Assessment Milestone Task Guidance