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Table of ContentsFacts
Number Stories
Subtraction Facts
Addition Facts
Mixed Addition and Subtraction Facts
Click on a topicto go to that section.
Recall from Memory
Presentation 1
Presentation 2
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Standards for Mathematical Practices
MP 8 Look for and express regularity in repeated reasoning.
MP 1 Make sense of problems and persevere in solving them.
MP 2 Reason abstractly and quantitatively.
MP 3 Construct viable arguments and critique the reasoning of others.
MP 4 Model with mathematics.
MP 5 Use appropriate tools strategically.
MP 6 Attend to precision.
MP 7 Look for and make use of structure.
Click on each standard to bring you to an example of how to meet
this standard within the unit.
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Students need to practice their facts. According to the Common Core (2.OA.2) they should be able to:
Fluently add and subtract within 20 using mental strategies. By the end of 2nd grade, know from memory
all sums of two one-digit numbers.
Facts
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This Facts unit addresses three underlying facets of addition/subtraction facts:
1. Building a deep understanding of the relationship between numbers in addition/subtraction problems.
2. Strategies for adding and subtracting.
3. Memorization of facts.
Facts
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The third topic - memorization - is most easily addressed through repeated practice of addition/subtraction problems.
This can be done through games, worksheets, or short timed quizzes (results would not count towards grades).
Facts
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Students should spend 1-10 minutes daily practicing adding and subtracting to build their memorization of these
facts.
In this way, this unit is slightly different in its layout from the rest of the PMI units.
The following pages list some resources for games, and worksheets that can be used for these purposes.
Facts
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- Printable Worksheets: Addition of One-Digit Numbers
Click the links below to find resources for worksheets and games:
- Adding with Cubes
- Addition Facts to 10
- Alien Addition
- Addition Patterns
- Counting On to Add
- Mummy Addition
- Sum Sense Timed Addition
Resources
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- How Many Under the Shell?
- Counting Back to Subtract
- Subtracting with Cubes
- Subtraction Patterns
- Sum Sense Timed Subtraction
Resources
Click the links below to find resources for worksheets and games:
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Addition Facts
Click to return to table of contents
Relationship of Whole to Parts: AdditionDefining and Identifying Whole and Parts
Addition Strategies
Making Tens
Adding 3 Numbers
Doubles FactsDoubles Plus 1Doubles Minus 1
Addition Strategies Adding Past 10
Making Tens Pt. 2
Lab: Add It Up
3 Addend Combinations
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Defining and Identifying Whole and Parts
Click to return to table of contents
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Whole and PartsActivity #1
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Whole and PartsActivity #2
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We have discovered that a whole can be one thing
that can be broken into parts...
Whole and Parts
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... or a whole can be a group of things
that can be broken into parts!
Whole and Parts
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When looking at a word problem, we need to figure out whether the numbers we know show the whole
number of things or the parts.
Word Problem
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Sarah was catching butterflies. She had 5 in her net. Then she caught some more. Now she has 8. How
many more butterflies did she catch?
Word Problem
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Juan was building with blocks. 2 of his blocks were yellow and 4 of his blocks were red. How many blocks
did he have in all?
Word Problem
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1 In the picture below, what is the whole number of flowers?
A 0
B 1
C 2
D 3
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2 How many flowers are in the part that is circled?
A 0
B 1
C 2
D 3
Ans
wer
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3 How many flowers are in the part that is NOT circled?
A 0
B 1
C 2
D 3
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8 Sam has 5 marbles. 2 of them are big and 3 of them are small.What is the whole number?
A 2
B 3
C 5
D 8
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9 Maria has 6 balloons. 2 of them are blue and 4 of them are red.What part of her balloons are red?
A 2
B 4
C 6
D 10
Ans
wer
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10 Jhamar had 3 pencils. His brother gave him 1 more. Now he has 4 pencils in all.What is the whole number of pencils he has?
A 1
B 3
C 4
D 8
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11 Lisa has 8 crayons. 6 of them are green and 2 of them are purple.What are the two parts in this problem?
A 8 crayons and 6 crayons
B 8 crayons and 2 crayons
C 6 crayons and 2 crayons
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Relationship of Whole to Parts:
Addition
Click to return to table of contents
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In order to understand how the whole number and the parts of a problem work together, we need to really
know what these symbols mean.
We use symbols when writing number sentences.
+ - =
Symbols
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We use the PLUS symbol to mean together with.
-+
We use the MINUS symbol to mean take away.
Symbols
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=We use the EQUAL SIGN to mean
the same total amount as.
It does NOT always mean "the answer is"!
Symbols
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You have probably seen many problems written like this.
1 + 3 = 4 Part Part Whole
Together with
Is the same total amount as
Symbols
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You may not have seen as many problems written like this.
4 = 1 + 3 PartPartWhole
Together with
Is the same total amount as
Is this problem correct? Can you explain why?
Symbols
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11 = 5 + 6
Identify parts of an addition sentence by dragging the titles to the correct location.
Part
Part
WholePlus Sign
Equal Sign
Addition Sentence
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Activity #1
Symbols
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Activity #2Symbols
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and
PART + PART = WHOLE
WHOLE = PART + PART
In this lesson, we have learned that:
Symbols
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12 Which of the following describes the picture below?
A 3 + 1 = 4
B 1 + 2 = 3
C 5 = 2 + 3
D 4 = 1 + 3
+
Ans
wer
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13 Which of the following also describes the picture below?
A 1 + 3 = 4
B 2 + 3 = 5
C 3 = 1 + 2
D 4 = 1 + 3
+
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15 Which of these number sentences could NOT describe the picture below?
A 2 = 3 + 1
B 1 + 2 = 3
C 3 = 2 + 1
D 2 + 1 = 3
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16 Which of the following number sentences is correct?
A 1 + 7 = 6
B 7 = 6 + 1
C 4 + 9 = 5
D 5 = 9 + 4
Ans
wer
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+1 2 3 54 6 7 8
Jason had 5 pieces of candy. Jeremy had 3 pieces of candy. How many pieces of candy did they have
altogether?
Draw a picture to help you count everything together.
5 + 3 = 8
Addition Strategies
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+
Does 3 + 5 = 8?
+
If 5 + 3 = 8
Addition Strategies
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+
Does 8 = 3 + 5?
+
If 8 = 5 + 3
Addition Strategies
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3 + 5 = 8
5 + 3 = 8
Turn Around Facts
Does it matter which addend is first?
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What are the turn around facts for:
3 4 7=+
+ =
+=
+=
Turn Around Facts
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7 2 =+ 9
+ =
+=
+=
What are the turn around facts for:
Turn Around Facts
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Addition problems can be written two ways.
5 + 3 = 8 or 5 + 3 8Horizontally
Vertically
Addition Problems
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4 + 2 =
Use a number line
Number Line Strategy
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+1 +24 + 2 =Number Grid Strategy
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Use Your Fingers
+
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Put the bigger number in your head and count up.
45, 6
4 + 2 =
Count Up
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56, 7
2 + 5 = turn it around to make it 5 + 2 =
Count UpIf the problem shows a small number first, reverse it and start with the bigger number in your head to make it easier to add.
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Susan had 6 pieces of candy. Her sister gave her 3 more. How many pieces of candy does she have now?
Make a Picture
=+
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Use a number line to add 6 + 3
Number Line
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6 + 3 =Number Grid Strategy
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6 + 3 =
6
Count Up
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Roll the dice and add the two numbers.
+
Pick a Strategy
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Interactive GameClick here for
the website
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18 ) 5 = 3 + 2
Yes
No
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19 ) 7 + 2 = 8
Yes
No
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20 Which is the correct answer?
43+
A 6
B 7
C 8
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21 Which is the correct answer?
5 + 1 =
A 5
B 6
C 7
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22
___ = 2 + 6
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23
4 5+
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24
3 + 3
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25
9 + 1 =
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There are 6 bees on one flower and 8 bees on another. How many bees are there altogether?
Addition Strategies
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Number GridUse a number grid - start with the bigger number and count up the smaller number.
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Jenna said she could do it in her head without a number grid. She said she will put the smaller number in her head and count up the larger number. Bob told her it would be easier to put the bigger number in her head and count up the smaller number. Who is correct?
Why?
Count Up
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6 + 8 = 14
Number Model
When you add two numbers together the answer is called the sum.
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What strategy
will you use?
Number model:
+ =
Pick a StrategyAnna had six read balloons and five blue balloons. How many balloons did she have altogether?
Teac
her N
otes
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What strategy
will you use?
Justin had 8 toy cars. He got 3 more for his birthday. How many does he have now?
Number model:
+ =
Pick a Strategy
Teac
her N
otes
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Flip two cards and add them together.
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Interactive GameClick here for
the website
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26 What is 9 + 2?
A 10B 11C 12
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27 What is 5 8+
A 13
B 14
C 15
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+ 28 9
4
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29 7 + 3 = ___
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30 ___ = 8 + 6
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31 7 8+
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3215 is the sum of which number model?
A 9 + 5
B 7 + 9
C 9 + 6
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3312 is the sum of which number model?
A 7 + 5
B 5 + 6
C 8 + 3
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34 What is the sum of 8 + 9?
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How many circles will fill up the frame?
Ten Frame
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When the frame is full, it will have ten objects in it.
When the frame is not full, it has less than 10 objects in it.
Ten Frames
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If 1 ten frame has 10 objects in it, how many objects are in 2 frames?
Ten Frames
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There are 7 books on the shelf. How many more are needed to fill the shelf?
7 + ___ = 10
Ten Frame
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How does this problem relate to what we have learned about adding parts together to make a whole number?
7 + ___ = 10
Ten Frame
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7 + 3 = 10What are three other ways we could write this?
Ten Frame
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6 + ___ = 10
6 children are on the bus. How many more need to get on?
Ten Frame
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8 + ___ = 10
8 horses are in the barn.How many are out in the field?
Ten Frame
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5 + ___ = 10
5 boys are on the basketball court.How many are on the bench?
Ten Frame
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3 + ___ = 10
3 cookies are left in the pack.How many have been eaten?
Ten Frame
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3 + 7 = 10
7 + 3 = 10
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Interactive GameClick here for the
website
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35 How many more objects are needed to make ten?
A 1
B 2
C 3
D 4
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36 How many more objects are needed to make 10?
A 3
B 4
C 5
D 6
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37 How many more objects are needed to make 10?
A 7
B 8
C 9
D 0
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38 Which number model does this ten frame show?
A 8 + 2 = 10
B 5 + 5 = 10
C 9 + 1 = 10
D 7 + 3 = 10
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39 This ten frame shows 6 + 4 = 10.
Yes
No
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40 Which number model does this ten frame show?
A 7 + 3 = 10
B 2 + 8 = 10
C 4 + 6 = 10
D 1 + 9 = 10
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A second ten frame can be used to help add numbers higher than 10.
10+
414
Number Model 10 + 4 = 14
2 Ten Frames
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Use the triangles to show the number 16.
10 + ___ = 16
What are the two parts in this problem?What is the whole number?
How do you know?
2 Ten Frames
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Use the triangles to show the number 12.
10 + ___ = 12
2 Ten Frames
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2 Ten FramesWhat addition sentence could you write
to match the ten frames?
______ + ______ = ______
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8 + 5 = ____
2
Start with the bigger addend. 8Think how many more do I need to make 10?Break apart the smaller addend 5 to help make the ten.
8 + 5 = ____<32
3
2 Ten Frames
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9 + 2 = ____
?
9 + 2 = ____<
??
2 Ten Frames
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6 + 7 = ____
?
6 + 7 = ____
?
2 Ten Frames
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Interactive GameClick here for a the
website
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41
9 + 8 =
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42
10 + 7 =
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43
8 6+
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44
5 + 9 =
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45
10 6+
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46
3 + 9 =
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What are some words or phrases you can think of that have the word
"double" in it?
Doubles
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A "doubles" fact in math is when you add a number to itself.
Doubles
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Doubles Facts from 1 to 10
1 + 1 = 22 + 2 = 4
4 + 4 = 85 + 5 = 106 + 6 = 127 + 7 = 148 + 8 = 169 + 9 = 18
3 + 3 = 6
10 + 10 = 20
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Double Factsby John Starkel
1 and 1 are 2,2 and 2 are 4,3 and 3 are 6,
Can you think of any more?4 and 4 are 8,5 and 5 are 10,6 and 6 are 12,
Here we go again!7 and 7 are 148 and 8 are 16,9 and 9 are 18,
Look, I’m an adding machine!Double facts are easy,
As easy as can be.Go back to the beginning,
And say this rhyme with me.
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1 + 1 = 2 eyes
Doubles
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2 + 2 = 4 wheels
Doubles
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3 + 3 6 pack
Doubles
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4 + 4 = 8 legs
Doubles
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5 + 5 10 fingers
Doubles
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6 + 6 = 12 eggs
Doubles
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7 + 7 14 days
1 2 3 4 5 6 7
8 9 10 11 12 13 14
Doubles
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8 + 8 = 16 crayons
Doubles
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9 + 9 18 squares
Doubles
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10 toes + 10 fingers 20
Doubles
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Tina is putting away books for her teacher. She has to put the same amount of books on each shelf.
There are 16 math books.
Tina puts _____ on one shelf.
She puts _____ on the other shelf.
Doubles
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There are 18 books about sports.
Tina puts _____ on one shelf.
She puts _____ on the other shelf.
Tina is putting away books for her teacher. She has to put the same amount of books on each shelf.
Doubles
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There are 12 art books.
Tina puts _____ on one shelf.
She puts _____ on the other shelf.
Tina is putting away books for her teacher. She has to put the same amount of books on each shelf.
Doubles
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47
+ =
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48
+ =
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49
+ =
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50 ) 9 + 9 =
A 10
B 18
C 17
D 16
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51 ) 4 + 4 =
A 4
B 6
C 8
D 10
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526 + 6 =
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532 + 2 =
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547 + 7 =
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4 and 5 are neighbors on the number line so they are a "doubles +1" fact.
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Doubles +1
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For "doubles + 1", double the smaller addend, then add 1.
4 + 5 =
4 + 4 + 1 =
Think, you know that 4 + 4 = 8, and one more is 9.
8 + 1 =
Doubles +1
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Are the addends neighbors?
I know 4+4=8.
I know 8+1=9
For "doubles + 1", double the smaller addend, then add 1.
Doubles +1
4 + 5 =
4 + 4 + 1 =
8 + 1 =
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2 + 3 =
Double the smaller addend, then add one.
4 + 1 = ___
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Doubles +1
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6 + 7 =
12 + 1 = ___
Double the smaller addend, then add one.
Doubles +1
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9 + 8 =
1 + 16 = ___
Even if the smaller number comes second in the fact, add it first.
Doubles +1
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6 + 5 =
1 + 10 = ___
Doubles +1
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What is the number model?
Roll the dice, double the number and add one.
Doubles +1
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Click the square, double the number and add one.
Doubles +1
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55 ) 8 + 7 = Doubles Plus One
1. Think: Are the addends neighbors?2. Double the smaller addend.
3. Add one.A 16
B 15
C 14
D 17
Hint
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56 ) 3 + 4 =
A 7
B 6
C 8
D 9
Doubles Plus One1. Think: Are the addends neighbors?
2. Double the smaller addend.3. Add one.
Hint
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57 5+ 6
A 10
B 12
C 11
D 13
Doubles Plus One1. Think: Are the addends neighbors?
2. Double the smaller addend.3. Add one.
Hint
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58 ) 1 + 2 = Doubles Plus One
1. Think: Are the addends neighbors?2. Double the smaller addend.
3. Add one.
Hint
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59
10+ 9
Doubles Plus One1. Think: Are the addends neighbors?
2. Double the smaller addend.3. Add one.
Hint
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60 ) 8 + 9 = Doubles Plus One
1. Think: Are the addends neighbors?2. Double the smaller addend.
3. Add one.
Hint
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4 and 5 are neighbors on the number line so they are a "doubles - 1" fact.
Doubles -1
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Are the addends neighbors?
I know 5+5=10.
I know 10-1=9
5 + 4 =
5 + 5 - 1 =
10 - 1 =
Doubles -1For "doubles - 1", double the larger addend, then subtract 1.
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5 + 4
Double 5 to get 10
10 - 1 = 9 so 5 + 4 = 9
Doubles -1
For "doubles - 1", double the larger addend, then subtract 1.
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4 + 3
4 + 4 = ___
___ - 1 = ___
Doubles Minus One1. Think: Are the addends neighbors?2. Double the larger addend.3. Subtract one.
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7 + 8
__ + __ = ___
___ - 1 = ___
fill in the blanks
Doubles Minus One1. Think: Are the addends neighbors?2. Double the larger addend.3. Subtract one.
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8 + 9
__ + __ = ___
___ - 1 = ___
fill in the blanks
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Click here for a doubles -1 song
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You can use dominos to help with doubles -1.
2 + 3 =
double 3, then -1
Doubles -1
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Use doubles -1 to solve.
3 + 4 =
Doubles -1
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4 + 5 =
Use doubles -1 to solve.
Doubles -1
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Use doubles -1 to match the addends with the correct sum.
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61 Double 7, then minus 1 = ?
Doubles Minus One1. Think: Are the addends neighbors?
2. Double the larger addend.3. Subtract one.
Hint
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62 Double 4, minus 1 = ?
Doubles Minus One1. Think: Are the addends neighbors?
2. Double the larger addend.3. Subtract one.
Hint
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63Solve:
8 + 9 =Doubles Minus One
1. Think: Are the addends neighbors?2. Double the larger addend.
3. Subtract one.
Hint
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64Solve:
6 + 7 =
Doubles Minus One1. Think: Are the addends neighbors?
2. Double the larger addend.3. Subtract one.
Hint
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65Solve:
5 + 6 =
Doubles Minus One1. Think: Are the addends neighbors?
2. Double the larger addend.3. Subtract one.
Hint
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Lab: Add It Up
This simple hands-on activity helps students master important addition facts and become strategic problem-
solvers!
Click here for complete directions.
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Megan made cupcakes with different colored icing. She made 2 pink cupcakes, 3 yellow cupcakes, and 5 purple cupcakes.
How many cupcakes did she make altogether?
2 + 3 + 5 =
Adding 3 Numbers
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What numbers would you add first? Why? Explain your thinking - there is
more than one good answer!
5 + 6 + 4 =
When adding three numbers, look for a combination of numbers that is easy to add first.
Adding 3 Numbers
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Finding a 10 fact is one strategy when adding 3 numbers.
5 + 6 + 4 =
5 + 10 = 15
Adding 3 Numbers
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You could also add the 2 bigger numbers first.
5 + 6 + 4 =
11 + 4 = 15
Adding 3 Numbers
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3 + 3 + 2 =
6 + 2 = 8
Once in a while, you might find a doubles fact you can use to help you.
Adding 3 Numbers
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6 + 4 + 4 =
In the basketball game Timmy scored 6 points, Chris scored 4 points and Vincent scored 4 points.
How many points did the team score altogether?
Pick a Strategy
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Roll the dice and add the three numbers.
Pick a Strategy
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664 + 2 + 7 =
A 11
B 12
C 13
D 14
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676 + 1 + 5 =
A 11
B 12
C 13
D 14
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68___ = 8 + 2 + 9
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693 + 7 + 3 =
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706 + 7 + 6 =
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What are some numbers we could put into this number model to
makeit correct?
4 + ___+ ___ = 10
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Different combinations of 3 numbers can add up to the same sum.
4 + 3 + 3 = 10
4 + 5 + 1 = 10
4 + 4 + 2 = 10
Combinations
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6 + ___+ ___ = 14
6 + ___+ ___ = 14
6 + ___+ ___ = 14
6 + ___+ ___ = 14
6 + ___+ ___ = 14
Can we find 5 ways to make this number sentence true?
Combinations
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Did we get them all?
6 + 5 + 3 = 14
6 + 4 + 4 = 14
6 + 8 + 0 = 146 + 7 + 1 = 14
6 + 6 + 2 = 14
Combinations
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8 + ___+ ___ = 17
8 + ___+ ___ = 17
8 + ___+ ___ = 17
8 + ___+ ___ = 17
8 + ___+ ___ = 17
Can we find 5 ways to make this number sentence true?Combinations
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8 + 8 + 1 = 17
8 + 5 + 4 = 17
8 + 9 + 0 = 178 + 6 + 3 = 17
8 + 7 + 2 = 17
Did we get them all?
Combinations
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Interactive GameClick here for the
website
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71 Which number sentence doesn't equal 18?
A 8 + 7 + 3
B 5 + 9 + 4
C 5 + 6 + 7
D 4 + 6 + 9
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72 Which number sentence doesn't equal 15?
A 7 + 2 + 6
B 7 + 2 + 7
C 5 + 8 + 2
D 4 + 6 + 5
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73 Which number sentence doesn't equal 13?
A 6 + 2 + 5
B 7 + 4 + 3
C 3 + 8 + 2
D 9 + 2 + 2
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74 What is the sum of 5 + 5 + 7?
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75 What is the sum of 2 + 3 + 4?
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76 What is the sum of 7 + 8 + 2?
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![Chapter 246-225 WAC RADIATION PROTECTION—X RAYS IN …leg.wa.gov/CodeReviser/WACArchive/Documents/2016/WAC 246 -225... · (6/26/08) [Ch. 246-225 WAC p. 1] Chapter 246-225 Chapter](https://static.documents.pub/doc/80x56/5c82589209d3f295198bd92e/chapter-246-225-wac-radiation-protectionx-rays-in-legwagovcodereviserwacarchivedocuments2016wac.jpg)
