CFISD First Grade Math
Strategies for Addition and Subtraction within 20
(Introduce Missing Part & Using Doubles)
Teacher Notes / Page #Unit Title / Doubles + 1
Doubles + 2
Addition with ten frames
Adding 3 numbers
Introducing Missing Part
More Missing Part
Doubles for Subtraction
Using a Number Line for Subtraction / 3
5
7
9
11
16
21
23
TEKS / The student is expected to:
1.3A use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99
1.3B use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4= ?; 3 + ? = 7; and 5= ?+5
1.3C compose 10 with 2 or more addends with and without concrete objects
1.3D apply basic fact strategies to add and subtract within 20, including making 10 and decomposing a number leading to a 10
1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences
1.3F generate and solve problem situations when given a number sentence involving addition or subtraction of numbers within 20
1.5F determine the unknown whole number in an addition or subtraction equation when the unknown may be any of the three or four terms in the equation
1.5G apply properties of operations to add and subtract two or three numbers
Vocabulary / Addition, Subtraction, Joining, Separating, Comparing, Equal, Sum, Difference, Doubles
Tips for Teachers / Essential Understandings are included for professional development purposes. To improve as math educators we must have a deep understanding of foundational math concepts.
Essential Understandings: Addition and its inversely related operation, subtraction, are powerful foundational concepts in mathematics, with applications to many problems situations and connections to many other topics.
Addition determines the whole in terms of the parts, and subtraction determines the missing part.
Fact Fluency / Please practice these activities that support the CFISD Fact Fluency Plan. All of the following activities can be found in the book Mastering the Basic Math Facts in Addition and Subtraction by O’Connell and Sangiovanni.
Hop the Line (p. 44)
Domino Addition (p. 59)
Ten More (p. 71)
Fill the Chart (p. 72) /
First Grade Teacher Notes
Strategies for Addition and Subtraction within 20
Doubles +1
TEKS:
1.3D apply basic fact strategies to add and subtract within 20
1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences
Materials:
Anchor chart doubles (Resource)
Doubles fact cards (Resource)
Unifix cubes
Three in a Row (Resource)
Doubles and Doubles +1 Practice Sheet (Resource)
Instruction:
Mathematicians, help me solve this problem:
Sara has 3 cookies. How many more cookies does she need to have 5?
Turn and tell your partner your thinking. You are doing a better job each day justifying your answers. I am proud of your mathematical thinking!
We have been learning the strategy of doubling a number to add two numbers which are the same. If we memorize our doubles, we will not have to count on our fingers or count manipulatives. We will know those facts quickly. I’m going to show you another way to use your doubles facts for more addition problems.
Travis has 4 Xbox games. He wants to save money for 5 more. How many games will he have in his collection?
You may know this answer because you know your facts to 10. You also know how to add 4 + 5 on the ten frame. You also know how to count 4 + 5 more on your fingers and other strategies. But this time use your doubles facts first. Which doubles facts would be helpful? (Wait for possible suggestions.)
4 + 4, right? OK, so 4 + 4=8 but he wants 5 more. So, if I know 4 + 4=8 then I would just count one more than 4 to get to 5. So I would say in my mind 8, 9. There will be 9 games in his collection. Using our doubles facts plus 1 more is another helpful strategy. We call it doubles +1.
Let’s try another:
Carol has 7 thank you notes. Her mother gives her 8 more to sign. How many thank you notes does she have altogether?
Let’s think together about how doubles may help us solve this problem quickly.
(Wait for any possible suggestions from your students.) I am thinking that I could possibly consider the numbers 7 + 7. If I know the doubles fact 7 + 7=14, I could add 1 more and that would be 15. I just count 14, 15. I don’t have to start back at 1 and count all the way from 1 to 7 and then 8 more. That is much faster! Let’s try another.
Bingo has 8 bones on Monday. On Tuesday he digs up 9 more. How many bones does Bingo have now?
Use your doubles facts first. Turn and tell your learning partner which doubles facts you are thinking will be the most helpful. (If students choose lower numbers such as 6 + 6, or 7+7, explain that they would want to choose one of the numbers in the problem. They may need this to be modeled with unifix cubes showing two sets; one with 8 and one with 9. Since you do not have 2 full groups of 9, you would choose the doubles fact for 8.) So we know 8+8=16 plus one more would be 17.
Turn and tell your learning partner why doubles and doubles plus 1 help us add bigger numbers. Point out to your students that the doubles + 1 strategy is most efficient when the numbers are very close together. For example, to solve 2 + 9, doubling 2 would not be very helpful or efficient. Ask the students to think about that and justify the reason. We want to teach them many different foundational strategies this year that they will decide if and when to use in the future.
Group #1: (Partner) Three in a Row (Resource) Students will select a doubles fact card and cover answer with a chip or cube. The object is to get three in a row on chart.
Group #2 (Independent) Doubles and Doubles +1 practice sheet.
Group #3 (Teacher directed-Small group) Practice doubles and doubles plus one problems with your students. Practice using the doubles strategies for both addition and subtraction problems.
First Grade Teacher Notes
Strategies for Addition and Subtraction within 20
Doubles +2
TEKS:
1.3D apply basic fact strategies to add and subtract within 20
1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences
Materials:
Doubles Anchor chart (resource)
Unifix cubes
White boards/markers
Doubles fact cards (resource)
Instruction:
Ready for mathematical thinking?
OK, try this:
Maria has 7 games. She gets 3 more. How many games does she have?
Turn and tell your partner what you are thinking.
Is it helpful to know the number bonds for ten? Did you use that strategy or did you use another like counting on?
Now think about this:
Maria has 10 games. She gives 3 of them to her friends. How many games does Maria have now?
Turn and tell your partner how you can use the addition sentence 7 + 3 = 10 from the first problem to help solve the second problem. Why does that work?
What are doubles facts? (Addition facts with the same addends) Why is 3 + 3 a doubles fact? (The addends are the same) What doubles facts do you know? Let’s review our Anchor chart for Doubles.
Today I want to show you another way doubles will help you add bigger numbers. And of course, if they help with addition, knowing doubles facts will help with subtraction.
I have 7 unifix cubes here. I have another group of 9 unifix cubes. If I want to know the total amount of unifix cubes I could count them one-by-one. Let me do that and you can time me. Have a student hold a timer and count the seconds or set a timer on your computer that projects to the whole class.
Count aloud as you stack each unifix cube; 1,2,3,4,5,6,7, (Exaggerate your counting to stress the point that counting by ones takes longer and is not efficient.)
8, 9, 10,11,12,13,14,15,16. OK stop the timer. How long did that take?
Record time on board.
Now let me use the doubles strategy for addition.
7 + 9 =?
7 + 7 =14 plus 2 more equals 16.
OK stop the timer. Record the time.
Which was quicker? Wow! I love Math! I love knowing different strategies so that I am even quicker and really thinking about numbers and how they work!
Did you notice that I couldn’t just use the doubles + 1 strategy that we talked about yesterday? I had 9 which is 2 more than 7 so I had to add my doubles plus 2.
That is what we will practice today.
Ann built two towers. One tower has 4 cubes. The other tower has 6 cubes. How many cubes did Ann use?
Use your doubles facts to begin. Now how many more do you need to add by counting on? Have students make the two towers with unifix cubes. Have them show two equal towers of 4. Then have them add the last two cubes to the tower.
Have them write the number sentence on the table or white board.
4 + 6 =10.
Have them write the strategy they used to solve.
I added double 4 and then counted on +2.
Jim built two towers. One tower has 7 cubes. The other tower has 9 cubes. How many cubes did Jim use?
Use your doubles facts to solve the problem. Write a sentence explaining which strategy you used.
Suzie built two towers. One tower had 6 cubes. The other tower had 8 cubes. How many cubes did Jim use?
Use your doubles facts to solve the problem. Write a sentence explaining which strategy you used.
Group #1: (Partner) Adding with Playing cards (Jacks, Queens and Kings=10)
Group #2 (Independent) Addition and Subtraction Practice Problems
Group #3 (Teacher directed-Small group) Practice adding doubles +1 and doubles +2.
First Grade Teacher Notes
Strategies for Addition and Subtraction within 20
Addition with ten frames
TEKS:
1.3A use concrete and pictorial models to determine the sum of a multiple of 10 and a one-digit number in problems up to 99
Materials:
Red and blue unifix cubes.
10 Ten frames (magnetic or drawn on chart or board)
Addition with Multiples of 10 Practice Sheet (Resource)
Instruction:
Today’s thinking problem is:
Mr. Teacher has two teams in his class. He asked Team A to solve 7 + 2. He asked Team B to solve 2 + 7. What answers did the two teams get? Why? Turn and tell your partner what you are thinking.
Ask one student to show the class 2 + 7 with red and blue unifix cubes. Ask another student to show the class 7+2 with the same blue and red unifix cubes. Why are both sets equal to 9?
They do not need to know that this is the commutative property, but understanding of the property will be developing.
Mathematicians, you are learning and using many strategies to add and subtract.
Today we will revisit our ten frames to add bigger numbers.
Show a ten frame on the board. Have students tell you how many are represented if all the spaces in the ten frame are filled.
Add dots to the second ten frame and choose different students to count the dots for the class. Focus on the numbers from 15-19 using the number sentences:
10+5=15.
10+6=16.
10+7=17.
10+8=18.
10+9=19.
Show additional ten frames and have students count by tens to 90.
Model the adding of multiples of ten plus a one-digit number. For example, 3 full ten frames equals 30, plus 2 dots in the fourth ten frame equals 32. If your teacher is 30 years old, in 2 more years he will be?
If your teacher is 70 years old, in 6 more years she will be?
7 full ten frames plus 6 dots in the eighth ten frame equals 76.
Model 29, 45, 91, and 87 writing the number sentences on the board such as 20 + 9=? 40+5=? 90 +1=? 80+7=?
Model number sentences written like this as well:
20
+4
Encourage students to use their subitizing skills to add these numbers, not one-by-one counting as much as possible.
If you have a multiple of ten such as 10, 20, 30, 40, 50, 60, 70, 80, or 90 plus another number you can use this strategy and add the numbers quickly in your head without a ten frame!
Group #1: (Partner) Three in a Row (Resource) same as yesterday
Group #2 (Independent) Addition with multiples of 10 Practice Sheet (Resource)
Group #3 (Teacher directed-Small group) Practice adding with multiples of 10. Have students make groups of ten (tens) with unifix cubes and single cubes. For example,
60 + 8-make 6 groups of ten and 8 singles. Have them count to ensure understanding of strategy. Record observations in monitoring notebook.
First Grade Teacher Notes
Strategies for Addition and Subtraction within 20
Adding 3 numbers
TEKS:
1.3C compose 10 with 2 or more addends with and without concrete objects
1.5G apply properties of operations to add and subtract two or three numbers
Materials:
3 different colors of unifix cubes
Addition with 3 Numbers Practice Sheet (resource)
Instruction:
Think about this: Mrs. Teacher has 2 students in her guided reading group. She asks 1 more to join the group. Then she asks 1 more student to join them. How many students are in the group now? Think about that…now turn and tell your learning partner what you are thinking.
Did you realize you can add 3 numbers together? Sometimes you might have to add 6 numbers together!! Wow!
Mrs. Principal might want to add all the students in the whole school!! She would need to add each group of students from each classroom. We have 60 classrooms here at our school so she would be adding 60 groups of numbers together. Amazing!! Our Principal needs to be very smart and a good math thinker!
Today we are just going to practice adding 3 numbers together.
Kelly sees 7 red birds. Bill sees 3 blue birds. Joe sees 1 yellow bird. How many birds do they see?
How many parts are in this story? (3) What is the addition sentence? 7 + 3 + 1 =?
Model solving this problem using red, blue, and yellow unifix cubes. Discuss different ways to add 3 addends. They may realize that 7 + 3 = 10 and add those two numbers first. They may need to count by ones adding the three groups as they count.
Help students connect the train to show that the sum does not change even if we count the three groups in different order.
(7 + 3) + 1 = 11 and 7 + (3 +1) = 11.
Essential Understandings:
The Associative Property for addition allows us to regroup addends; it is generally stated formally as follows:
a + (b + c) = (a +b) + c
Being able to use the associative property fluently is important in developing good number sense.
Breanna collected 4 red marbles. She buys 4 purple marbles and 2 blue marbles.
How many marbles does Breanna have?
Show me how to solve this problem using 3 different colors of unifix cubes. Which two sets will you add together first? Does knowing the doubles fact for 4 help you here?
Or did you solve the problem another way?
Group #1: (Partner) Doubles fact cards- practice with your partner
Group #2 (Independent) Addition and Subtraction practice problems
Group #3 (Teacher directed-Small group) Practice adding with 3 numbers. Encourage the use of different strategies to be most effective problem solvers.
First Grade Teacher Notes
Strategies for Addition and Subtraction within 20
Introducing Missing Part
TEKS:
1.3B use objects and pictorial models to solve word problems involving joining, separating, and comparing sets within 20 and unknowns as any one of the terms in the problem such as 2 + 4= ?; 3 + ? = 7; and 5=? +5
1.3E explain strategies used to solve addition and subtraction problems up to 20 using spoken words, objects, pictorial models, and number sentences
1.5F determine the unknown whole number in an addition or subtraction equation when the unknown may be any of the three or four terms in the equation
Materials:
2-color counters
Student copies of the story problems
Instruction:Mathematicians, help me solve this problem:
Superman rescued 18 people from danger. If he rescued 9 children, how many adults did he rescue? Take a minute to think about your answer. Just use all you know about numbers and mathematics, do not use a pencil, just your brain.
Now turn and tell your learning partner what your answer is. You will need to justify your answer; that means to explain what you were thinking about to solve the problem. If your learning partner has a different answer, that is OK. Maybe if you are able to explain and justify your thinking, she will agree with you and learn from your thinking.