Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

Pre-K-2
1

Students practice their addition facts for sums up to 12 by playing a game. They add to their personal addition charts. Students are encouraged to practice the facts that they have not yet mastered. Finally, triangular flash cards help students practice addition facts.

Put students in pairs, and provide them with two number cubes and a game board for Cover Up.

To play the game:
1. Each student chooses a section of the game board.
2. When it is your turn, roll the two number cubes and find the sum of the two numbers that come up.
3. Cover up the number on your part of the board for that sum, if it's not yet covered up.
4. Then, it's the other player's turn.
5. The first students to cover up all 11 numbers is the winner.
6. When one student wins, the pair should remove all the counters and play again.

Continue the lesson by having each student review his or her copy of the Facts I Know Activity Sheet, adding known facts as necessary. Then display a large copy of an addition chart on the board or overhead. Call on volunteers to come to the front and circle one fact that they have studied so far.

When the students have circled all the facts that they have studied, direct their attention to the facts that are left:

4 + 9
5 + 8, 5 + 9
6 + 7, 6 + 8, 6 + 9
7 + 6, 7 + 8, 7 + 9
8 + 5, 8 + 6, 8 + 7, 8 + 9
9 + 4, 9 + 5, 9 + 6, 9 + 7, and 9 + 8

Ask the class what they know that will help them learn fewer than 18 facts. Encourage them to remember the commutative property.

Remind the students that some of these facts belong to the doubles-plus-one group. Ask them to identify them. [These facts are 6 + 7, 7 + 8, and 8 + 9.] Now circle in another color the remaining six facts: 4 + 9, 5 + 8, 5 + 9, 6 + 8, 6 + 9, and 7 + 9.

Place the students in pairs and assign each student three addition facts from the following: 4 + 9, 5 + 8, 5 + 9, 6 + 8, 6 + 9, 7 + 9, as a set of demonstration facts. Have the students cut two triangular shapes from each of three index cards. Demonstrate how to make a triangular flash card by putting the two addends in two of the corners and the sum in the other corner, as in the example below.

Now ask the students to make triangular fact cards for the facts they choose, then trade the cards with their partner. Ask each student to cover the sum on one card with his or her thumb, show the card to the other student, and ask him or her to tell the sum.

Conclude the lesson by asking students to be sure that they have covered both facts in a commutative pair [For example, 6 + 7 and 7 + 6.]. Finally, ask them to choose two facts and make triangular flash cards for them. Encourage the students to take those two new cards and the three they made in this lesson home to practice.

Assessment Option

The students will vary in how quickly they attain command of the addition facts at the immediate-recall level. Therefore, you may find your entries in the Class Notes recording sheet especially helpful in grouping students for remedial instruction. This information may also be helpful in deciding on appropriate homework assignments.
Extension
Move on to the last lesson, Wrapping Up the Unit.

Questions for Students

1. What sums can you get when you roll two number cubes? How can you get three as a sum? How can you get eleven as a sum? Seven as a sum? Eight as a sum?

[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; 1+2; 5+6; 1+6, 2+5; 2+6, 3+5, 4+4.]

[The sum is one more than the other addend; The sum is the other addend.]

3. What doubles can you get with number cubes?

[2, 4, 6, 8, 10, 12.]

4. What pairs of numbers have a sum of 12? 18? Are any of these pairs doubles? What other doubles have you studied?

[0+12, 1+11, 2+10, 3+9, 4+8, 5+7, 6+6; 0+18, 1+17, 2+16, 3+15, 4+14, 5+13, 6+12, 7+11; 8+10, 9+9; Yes, 6+6 and 9+9 are doubles.]

5. What pairs of numbers have a sum of 13? Of 15? Of 17

[0+13, 1+12, 2+11, 3+10, 4+9, 5+8, 6+7; 0+15, 1+14, 2+13, 3+12, 4+11, 5+10, 6+9; 7+8; 0+17, 1+16, 2+15, 3+14, 4+13, 5+12, 6+11, 7+10, 8+9.]

Teacher Reflection

• Which students have only a few addition facts learned? What activities should I plan for them?
• What extension activities are appropriate for the students who have learned all their addition facts?
• What adjustments will I make the next time that I teach this lesson?
• Which students are able to identify the facts they have learned? How can others be helped to achieve this goal?
• Which students have only a few addition facts left to learn? What activities should I plan for them?

Pre-K-2
A game encourages students to find the sums of two one-digit numbers. Students explore commutativity and examine patterns on an addition table. They then use a personal addition chart to record and keep track of known facts.

Finding Sums to Six

Pre-K-2
In this lesson, students discover the role of the additive identity and explore sums to six. They continue to complete their personal addition charts.

Some Special Sums

Pre-K-2
Students practice doubles and doubles-plus-one addition facts. They record their current level of mastery of the addition facts on their personal addition charts.

Wrapping up the Unit

Pre-K-2
In this final lesson of the unit, students display their knowledge of properties of objects for sorting and creating patterns. They also demonstrate an understanding of commutativity and model addition and subtraction of whole numbers using different representations.

Learning Objectives

Students will:

• Practice addition facts up to 12.
• Create a learning tool for memorizing the rest of the addition facts.

NCTM Standards and Expectations

• Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
• Develop fluency with basic number combinations for addition and subtraction.

Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

• CCSS.Math.Content.K.OA.A.5
Fluently add and subtract within 5.

• CCSS.Math.Content.1.OA.B.4
Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

• CCSS.Math.Content.1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

• CCSS.Math.Content.1.NBT.C.4
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.

• CCSS.Math.Content.2.OA.B.2
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

• CCSS.Math.Content.2.NBT.B.5
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• CCSS.Math.Content.2.NBT.B.6
Add up to four two-digit numbers using strategies based on place value and properties of operations.
The text passage describes a lesson plan for teaching addition facts to young students, including a game called "Cover Up" and the creation of triangular flash cards. It also includes a set of questions for students and a section for teacher reflection.
multiple_questions

the passage contains multiple mathematical questions in the "questions for students" section, but no answers are provided within the text.
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
Thank you for your interest in NCTM’s Illuminations. Beginning in mid-April, all Illuminations content will be moving to nctm.org/illuminations. Interactives will remain openly available and NCTM members will have access to all Illuminations lessons with new filtering and search options. We hope you will continue to utilize and enjoy these resources on nctm.org.

Pre-K-2
1

Students practice their addition facts for sums up to 12 by playing a game. They add to their personal addition charts. Students are encouraged to practice the facts that they have not yet mastered. Finally, triangular flash cards help students practice addition facts.

Put students in pairs, and provide them with two number cubes and a game board for Cover Up.

To play the game:
1. Each student chooses a section of the game board.
2. When it is your turn, roll the two number cubes and find the sum of the two numbers that come up.
3. Cover up the number on your part of the board for that sum, if it's not yet covered up.
4. Then, it's the other player's turn.
5. The first students to cover up all 11 numbers is the winner.
6. When one student wins, the pair should remove all the counters and play again.

Continue the lesson by having each student review his or her copy of the Facts I Know Activity Sheet, adding known facts as necessary. Then display a large copy of an addition chart on the board or overhead. Call on volunteers to come to the front and circle one fact that they have studied so far.

When the students have circled all the facts that they have studied, direct their attention to the facts that are left:

4 + 9
5 + 8, 5 + 9
6 + 7, 6 + 8, 6 + 9
7 + 6, 7 + 8, 7 + 9
8 + 5, 8 + 6, 8 + 7, 8 + 9
9 + 4, 9 + 5, 9 + 6, 9 + 7, and 9 + 8

Ask the class what they know that will help them learn fewer than 18 facts. Encourage them to remember the commutative property.

Remind the students that some of these facts belong to the doubles-plus-one group. Ask them to identify them. [These facts are 6 + 7, 7 + 8, and 8 + 9.] Now circle in another color the remaining six facts: 4 + 9, 5 + 8, 5 + 9, 6 + 8, 6 + 9, and 7 + 9.

Place the students in pairs and assign each student three addition facts from the following: 4 + 9, 5 + 8, 5 + 9, 6 + 8, 6 + 9, 7 + 9, as a set of demonstration facts. Have the students cut two triangular shapes from each of three index cards. Demonstrate how to make a triangular flash card by putting the two addends in two of the corners and the sum in the other corner, as in the example below.

Now ask the students to make triangular fact cards for the facts they choose, then trade the cards with their partner. Ask each student to cover the sum on one card with his or her thumb, show the card to the other student, and ask him or her to tell the sum.

Conclude the lesson by asking students to be sure that they have covered both facts in a commutative pair [For example, 6 + 7 and 7 + 6.]. Finally, ask them to choose two facts and make triangular flash cards for them. Encourage the students to take those two new cards and the three they made in this lesson home to practice.

Assessment Option

The students will vary in how quickly they attain command of the addition facts at the immediate-recall level. Therefore, you may find your entries in the Class Notes recording sheet especially helpful in grouping students for remedial instruction. This information may also be helpful in deciding on appropriate homework assignments.
Extension
Move on to the last lesson, Wrapping Up the Unit.

Questions for Students

1. What sums can you get when you roll two number cubes? How can you get three as a sum? How can you get eleven as a sum? Seven as a sum? Eight as a sum?

[2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12; 1+2; 5+6; 1+6, 2+5; 2+6, 3+5, 4+4.]

[The sum is one more than the other addend; The sum is the other addend.]

3. What doubles can you get with number cubes?

[2, 4, 6, 8, 10, 12.]

4. What pairs of numbers have a sum of 12? 18? Are any of these pairs doubles? What other doubles have you studied?

[0+12, 1+11, 2+10, 3+9, 4+8, 5+7, 6+6; 0+18, 1+17, 2+16, 3+15, 4+14, 5+13, 6+12, 7+11; 8+10, 9+9; Yes, 6+6 and 9+9 are doubles.]

5. What pairs of numbers have a sum of 13? Of 15? Of 17

[0+13, 1+12, 2+11, 3+10, 4+9, 5+8, 6+7; 0+15, 1+14, 2+13, 3+12, 4+11, 5+10, 6+9; 7+8; 0+17, 1+16, 2+15, 3+14, 4+13, 5+12, 6+11, 7+10, 8+9.]

Teacher Reflection

• Which students have only a few addition facts learned? What activities should I plan for them?
• What extension activities are appropriate for the students who have learned all their addition facts?
• What adjustments will I make the next time that I teach this lesson?
• Which students are able to identify the facts they have learned? How can others be helped to achieve this goal?
• Which students have only a few addition facts left to learn? What activities should I plan for them?

Pre-K-2
A game encourages students to find the sums of two one-digit numbers. Students explore commutativity and examine patterns on an addition table. They then use a personal addition chart to record and keep track of known facts.

Finding Sums to Six

Pre-K-2
In this lesson, students discover the role of the additive identity and explore sums to six. They continue to complete their personal addition charts.

Some Special Sums

Pre-K-2
Students practice doubles and doubles-plus-one addition facts. They record their current level of mastery of the addition facts on their personal addition charts.

Wrapping up the Unit

Pre-K-2
In this final lesson of the unit, students display their knowledge of properties of objects for sorting and creating patterns. They also demonstrate an understanding of commutativity and model addition and subtraction of whole numbers using different representations.

Learning Objectives

Students will:

• Practice addition facts up to 12.
• Create a learning tool for memorizing the rest of the addition facts.

NCTM Standards and Expectations

• Develop and use strategies for whole-number computations, with a focus on addition and subtraction.
• Develop fluency with basic number combinations for addition and subtraction.

Common Core State Standards – Mathematics

-Kindergarten, Algebraic Thinking

• CCSS.Math.Content.K.OA.A.5
Fluently add and subtract within 5.

• CCSS.Math.Content.1.OA.B.4
Understand subtraction as an unknown-addend problem. For example, subtract 10 - 8 by finding the number that makes 10 when added to 8.

• CCSS.Math.Content.1.OA.C.6
Add and subtract within 20, demonstrating fluency for addition and subtraction within 10. Use strategies such as counting on; making ten (e.g., 8 + 6 = 8 + 2 + 4 = 10 + 4 = 14); decomposing a number leading to a ten (e.g., 13 - 4 = 13 - 3 - 1 = 10 - 1 = 9); using the relationship between addition and subtraction (e.g., knowing that 8 + 4 = 12, one knows 12 - 8 = 4); and creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating the known equivalent 6 + 6 + 1 = 12 + 1 = 13).

• CCSS.Math.Content.1.NBT.C.4
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.

• CCSS.Math.Content.2.OA.B.2
Fluently add and subtract within 20 using mental strategies. By end of Grade 2, know from memory all sums of two one-digit numbers.

• CCSS.Math.Content.2.NBT.B.5
Fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• CCSS.Math.Content.2.NBT.B.6
Add up to four two-digit numbers using strategies based on place value and properties of operations.
user
The text passage describes a lesson plan for teaching addition facts to young students, including a game called "Cover Up" and the creation of triangular flash cards. It also includes a set of questions for students and a section for teacher reflection.

TYPE: MULTIPLE_QUESTIONS

The passage contains multiple mathematical questions in the "Questions for Students" section, but no answers are provided within the text.