## Finding Sums to Six

Pre-K-2
1

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

Call the students together and ask for a volunteer. Have that student roll a single number cube and record the number that came up. Now ask what number must be rolled for a total of six. [If a six was rolled the first time, the student should report that no further rolls are necessary.] Then have the student record the number sentence on the board [6 + 0 = 6.] Repeat with other volunteers.

Ask what addition fact would represent a roll of one and a roll of five. [1 + 5 = 6.] Then ask what addition fact would represent a roll of six and no further rolls. [6 + 0 = 6.] You may want to mention that zero is known as the additive identity, and you may want to ask students why they think that zero has this name. [The sum when any number is added to zero is itself, so it is "identical."]

Now ask the students to take out their Facts I Know Activity Sheets they began completing in the previous lesson, Finding Addition Patterns. Ask what addition facts they can be sure of, if they know that any number plus zero is the number that they started with. Have the students fill in those facts on their personal addition charts. Then ask them what happens when they add one to a number. [They may suggest it is like counting on to the next number.] If they can answer correctly, have them enter these facts on their charts as well. This will significantly reduce the number of facts that need to be learned separately. Note that as a student begins to identify patterns, they will be able to complete large portions of their addition charts. A partially completed chart is shown below.

 + 0 1 2 3 4 5 6 7 8 9 0 0 1 2 3 4 5 6 7 8 9 1 1 2 3 4 5 6 7 8 9 10 2 2 3 6 3 3 4 10 4 4 5 6 5 5 6 10 6 6 7 12 7 7 8 10 16 8 8 9 9 9 10 16

To give students a chance to practice the sums to six, assign them to pairs and give each pair two number cubes. Tell them that the goal of the game they will play is to make sums of six. Ask them to take turns rolling the number cubes and giving themselves a tally mark each time the sum is six. Allow them time to play the game, then call them together and tell them that you will name a number less than six and they should raise their fingers to show how many more are needed to make six. Play this game several times, then ask volunteers to list on the board all the ways they can get six when they roll a pair of number cubes. [0 + 6, 1 + 5, 2 + 4, 3 + 3.] Invite the students to add as many of these facts as they know by heart to their personal addition charts.

To conclude this lesson, have students record, on paper, a picture of two number cubes showing a sum of six.

Assessment Option

You may wish to add your observations on the students' current level of mastery of the addition facts to the Class Notes recording sheet. You may find the information useful when providing input for planning remedial and enrichment learning experiences.

Extension

Move on to the next lesson, Some Special Sums.

Questions for Students

1. If you rolled a five, what would you need to roll to make a sum of six? What addition fact would show that?

[1; 5 + 1 = 6.]

2. If you rolled a one, what would you need to roll to make a sum of six? What addition fact would show that? What is alike between this addition sentence and the one you wrote for the other example? What is different? How can this help you learn your addition tables by heart?

[5; 1 + 5 = 6; the addition sentences have the same addends and sum; the addends are in reverse order.]

3. How many ways can you roll a sum of six with two number cubes? How many ways can you have a sum of five? Of four? Of one?

[3 different ways: 1+5, 2+4, 3+3; 2 different ways: 1+4, 2+3; 2 different ways: 1+3, 2+2; A sum of one cannot be obtained from a roll of two number cubes.]

Teacher Reflection

• Which students are able to identify with accuracy the facts they know by heart? How can the other students be helped to do this?
• Which students were able to stay on task while they played the game? Should some pairs be changed in the next lesson?
• 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?

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.

### 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.

Pre-K-2
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.

### 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:

• Explore the results of adding zero.
• Find pairs of addends that have a sum of six.
• Practice the addition facts with sums to six.

### NCTM Standards and Expectations

• Understand the effects of adding and subtracting whole numbers.
• 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.