PRINT VERSION - Partitions of Ten

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Summary

Students will learn a variety of ways to compose and decompose ten. Students will work with a variety of representations such as finger patterns, ten frames, number paths, and stories to help recognize and use pairs of numbers that add together to equal ten.

Goals and Standards

Colorado Academic Standards:

K.OA.A. Operations & Algebraic Thinking: Model and describe addition as putting together and adding to, and subtraction as taking apart and taking from, using objects or drawings.
1.OA.C. Operations & Algebraic Thinking: Add and subtract within 20.

Mathematical Practice Standards:

MP4. Model with mathematics.
MP5. Use appropriate tools strategically.
MP6. Attend to precision.
MP7. Look for and make use of structure.

Learning Goal:

Students compose and decompose ten in a variety of ways.
Students flexibly solve a variety of addition and subtraction problem types such as additive, subtractive, missing addend, and missing subtrahend within ten.

Materials List

Blue and red ten frame cards (Ten Frame Cards)

Partitions of ten addition equation cards (Addition Equation Cards)
Subtraction within ten equation cards (Subtraction Equation Cards)
Jumps on number line board (Number Line Board)
Ten small objects such as counters, paper clips, pennies, etc
Small opaque cup
Six-sided Dice

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Progression of Skills (outline)

Before the lesson:

Before the lesson: Students know partitions of 5, or the combinations of 2 numbers that add together to make 5.

During this toolkit lesson:

Students are working on partitions of 10, or the combinations of 2 numbers that add together to make 10.

After the lesson:

Students use partitions of ten to solve addition and subtraction beyond 10.

Lesson Introduction and Pre-Assessment

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Pre-assessment and answer key:

Give the following tasks verbally as an interview. Do not provide materials such as a number line or counters. Students may use their fingers as support.

If I have 4 cookies, how many more do I need to have 5 cookies.
- 1 more cookie to have 5
- Make a note of the student’s thought process, if they are counting up to solve this problem or if they use a known fact to answer this question.
If I have 2 cookies, how many more do I need to have 5 cookies?
- 3 more cookies to have 5
- Make a note of the student’s thought process, if they are counting up to solve this problem or if they use a known fact to answer this question.
Can you tell me two numbers that add together to make five? Can you tell me two more?
- Range of possible answers that are all acceptable as long as they add together to equal five.
- If a student says 5+0 or 0+5, ask for another combination of numbers. If both answers are commutative, meaning they use the same numbers but in a different order such as 2+3 and 3+2, ask for another combination to five. If a student is unable to give 2 combinations to make five they will need support with partitions of five before working with ten.
Students will be more fluent with partitioning to 10 if they are fluent working with five. If the student solved each of these questions by counting each of their fingers, or counting on, they are not yet fluent with their facts within 5. This toolkit can be used with partitions of 5 instead of ten.

Warm Up / Activation of Learning: Finger Patterns

With the student’s hands visible, “Can you show me 4 on your fingers as quickly as you can?” Repeat this questioning for the numbers 2, 5, 6, 8, 3, 9, 10, 7.
- During this activity look to see if the student is raising their fingers simultaneously or sequentially. If they raise fingers sequentially, ask them if they can raise their fingers all at once.
- Extension: Ask the student “Is there another way to make 4?”
- If making a second finger combination is too challenging, continue by only asking for one finger pattern for each number.
- Extension: Students can also be asked to hold their hands over their head when making finger patterns.
Start with fingers visible and on the table. Ask the child to show 8 on their fingers. “How many fingers are up? How many fingers are down? How many fingers do you have all together?”
- Repeat this line of questioning with 6, 9, 7, 5, 4, 2, 3 and 1.
- This activity can also be repeated with student’s hands over their head as an extension.
- This activity allows students to experience the part-part-whole relationships within ten, using their fingers.

Lesson Session 1

Read the teacher's guides for directions for each session.

Warm Up / Activation of Learning: Finger Patterns

With the student’s hands visible, “Can you show me 4 on your fingers as quickly as you can?” Repeat this questioning for the numbers 2, 5, 6, 8, 3, 9, 10, 7.
- During this activity look to see if the student is raising their fingers simultaneously or sequentially. If they raise fingers sequentially, ask them if they can raise their fingers all at once.
- Extension: Ask the student “Is there another way to make 4?”
- If making a second finger combination is too challenging, continue by only asking for one finger pattern for each number.
- Extension: Students can also be asked to hold their hands over their head when making finger patterns.
Start with fingers visible and on the table. Ask the child to show 8 on their fingers. “How many fingers are up? How many fingers are down? How many fingers do you have all together?”
- Repeat this line of questioning with 6, 9, 7, 5, 4, 2, 3 and 1.
- This activity can also be repeated with student’s hands over their head as an extension.
- This activity allows students to experience the part-part-whole relationships within ten, using their fingers.

Anticipate Misconceptions:

Students may need to recount the collection they are working with for each task given. For example when doing ten frame cards, students may need to count the total number of dots on the card each time they see a new card. Give students the opportunity to count the collection to reinforce that the quantity of the collection remains the same. Be sure to reinforce with questioning to develop this concept.
Counting by ones to solve within the range of ten may be necessary for students to develop their understanding of quantities up to ten. Allow students the opportunity to count as needed. Students will move towards automaticity with more practice. Do not expect automaticity immediately because that will often encourage a student to memorize their facts rather than develop relational thinking around the facts they are working on.
Some students might struggle with counting on a number line versus the dots on a ten frame or the counters in the cup. It’s important to support kids with when and where they are starting and ending the count.

Optional Activities:

Review of area and perimeter of rectangles
Desmos for review of order of operations
Review of Fractions, Decimals and Percents
Tax Tip Discount practice
Error Analysis for distribution and combining like terms

Progress Monitoring:

Listening for misconceptions during student dialogue
Attending to the claims initially made during each task
Asking questions to clarify thinking and correct misconceptions
Using pre and post assessments to document mastering and identify needed clarification.

Lesson Closure and Post-Assessment

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Directions for Lesson Closure:

Student created stories: Instruct students to pick a ten frame card and create a story to match that card.
- For example, display the ten frame card with 7 blue dots and 3 red dots.
  - One possible student response could be “I have 10 pets, 7 are dogs and 3 are cats.”
Adult-led questioning: “I picked ten flowers, some were red and some were blue. If those were the only colors of flowers, what combinations of red and blue flowers could I have?”

Post-assessment and answer key:

Give the following tasks verbally as an interview. Do not provide materials such as a number line or counters. Students may use their fingers as support.
I went apple picking yesterday and picked ten apples, each either red or yellow. What are some combinations of red and yellow apples that I could have?
- Range of possible answers that are all acceptable as long as they add together to equal ten.
If 7 of the apples I picked were yellow, how many would be red? How did you get that answer?
- Correct Answer: 3
- Make a note of the student’s thought process, if they are counting up to solve this problem or if they use a known fact to answer this question.
If 4 apples were red, how many apples would be yellow? How did you get that answer?
- Correct Answer: 6
- Make a note of the student’s thought process, if they are counting up to solve this problem or if they use a known fact to answer this question.
After picking my ten apples, 2 fell out of my bag and rolled away. How many apples are left in my bag? How did you think about this question?
- Correct Answer: 8
- Make a note of the student’s thought process, if they are counting up to solve this problem or if they use a known fact to answer this question.
Challenge - If 4 apples were red in my bag and my friend ate a yellow apple and I ate a red one, how many of each color are left?

Real-World Applications and Project Ideas

A globe with tools such as a map and measuring cup surrounding its border.

They can work on partitions of other numbers, e.g., What are the partitions of 8?
Human number line game. Play the number line game but instead of using a number line on a piece of paper, draw a giant number line on the ground with chalk and take steps on the number line instead of moving a counter.
Dominos: Using a set of dominos, make a train of dominos by connecting ends of dominos that add together to equal ten.
Desmos Activity Grade 2: Ways to Make 10 Desmos Activity Link
- Preview the Teacher Guide (at the top right of the screen) to prepare for the activity. You will need to create a (free) teacher account in order to assign the activity to your students. Alternatively, students can complete the activity in preview mode without creating an account.
- Assign to your class or use a single session code. The Desmos activity may be completed as a single student, but if a class of students all completes the activity, it will share some data with them about their results as a class.
Make 10 Go Fish: Using a deck of playing cards, keep the Ace and remove the remaining face cards. Play Go Fish making pairs to 10 instead of matching pairs.

Sources:

https://link.springer.com/article/10.1007/s10649-019-09927-1
Figuring Out Fluency in Mathematics by Jennifer Bay-Williams and John SanGiovann
Teaching Number: Advancing Children’s Skills and Strategies by Robert Wright, Jim Martland, Ann Stafford, Gary Stanger
Teaching Number in the Classroom with 4-8 year olds by Robert Wright, Jim Martland, Ann Stafford, Gary Stanger