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."]
Facts I Know Activity Sheets
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?
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.
Grade 1, Algebraic Thinking
- 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.
Grade 1, Algebraic Thinking
- 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).
Grade 1, Number & Operations
- 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.
Grade 2, Algebraic Thinking
- 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.
Grade 2, Number & Operations
- 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.
Grade 2, Number & Operations
- CCSS.Math.Content.2.NBT.B.6
Add up to four two-digit numbers using strategies based on place value and properties of operations.
Grade 2, Number & Operations
- CCSS.Math.Content.2.NBT.B.7
Add and subtract within 1000, 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. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.
Grade 2, Number & Operations
- CCSS.Math.Content.2.NBT.B.9
Explain why addition and subtraction strategies work, using place value and the properties of operations.
Common Core State Standards – Practice
- CCSS.Math.Practice.MP6
Attend to precision.