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1
Second Grade
Parent Math Information
Information gathered by 2nd Grade Teachers
(all trained Cognitively Guided Instruction teachers)
Common Core National Math
Standards (College and Career Readiness Standards)
v
2010 Arizona Math Standards
v
Kyrene Math Standards
2
http://www.azed.gov/azcommoncore/families/
Your child is learning:
Times have changed…
Today’s students must master
advanced skills in mathematics,
science, and technology to stay on
track for college and for promising
careers. Mathematics teaches ways
of thinking that are essential to
work and civic life.
3
*Students who take algebra and geometry go on to college at
much higher rates than those who do not (83% vs. 36%).
*Most four-year colleges require three to four years each of
high school math and science for admission.
*Almost 90% of all new jobs require math skills beyond the
high school level
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Second Grade- Five Domains
Operations and Algebraic Thinking
Numbers in Base Ten
Geometry
Measurement and Data
Mathematical Practices
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Mathematical Practices 1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of
others.
4. Model with mathematics.
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
We teach problem solving to help improve:
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Your child using mathematical procedures in the classroom…
7
Your child using mathematical procedures in the classroom…
8
Common Addition and Subtraction Situations Result Unknown Change Unknown Start Unknown
Add to
Two bunnies sat on the
grass. Three more bunnies
hopped there. How many bunnies are on the grass now?
2 + 3 = ?
Two bunnies were sitting
on the grass. Some more bunnies hopped there.
Then there were five bunnies. How many bunnies hopped over to
the first two? 2 + ? = 5
Some bunnies were sitting
on the grass. Three more bunnies hopped there.
Then there were five bunnies. How many bunnies were on the grass
before? ? + 3 = 5
Taken from
Five apples were on the table. I ate two apples.
How many apples are on the table now? 5 – 2 = ?
Five apples were on the table. I ate some apples.
Then there were three apples. How many apples did
I eat? 5 – ? = 3
Some apples were on the table. I ate two apples.
Then there were three apples. How many apples were on the table before?
? – 2 = 3
Put
Together/ Take Apart2
Total Unknown Addend Unknown Both Addends Unknown1
Three red apples and two green apples are on the table. How many
apples are on the table? 3 + 2 = ?
Five apples are on the table. Three are red and the
rest are green. How many apples are green?
3 + ? = 5, 5 – 3 = ?
Grandma has five flowers. How many can she put in her red vase and how
many in her blue vase? 5 = 0 + 5, 5 = 5 + 0
5 = 1 + 4, 5 = 4 + 1 5 = 2 + 3, 5 = 3 + 2
Compare3
Difference Unknown Bigger Unknown Smaller Unknown
(“How many more?”
version): Lucy has two apples.
Julie has five apples. How many more apples does Julie have than
Lucy?
(“How many fewer?” version): Lucy has two apples.
Julie has five apples. How many fewer apples
does Lucy have than Julie? 2 + ? = 5, 5 – 2 = ?
(Version with “more”):
Julie has three more apples than Lucy. Lucy
has two apples. How many apples does Julie have?
(Version with “fewer”):
Lucy has 3 fewer apples than Julie. Lucy has two apples.
How many apples does Julie have?
2 + 3 = ?, 3 + 2 = ?
(Version with “more”):
Julie has three more apples than Lucy. Julie has five
apples. How many apples does Lucy have?
(Version with “fewer”): Lucy has 3 fewer apples
than Julie. Julie has five apples. How many apples does
Lucy have? 5 – 3 = ?, ? + 3 = 5
Your child is
expected to
know how
to solve 12
different
types of
problems.
Operations and Algebraic Thinking
Mental Math Strategies through 20
*Plus 0 9+0=9
*Counting On/Counting Back
7+2~ 7, 8, 9; 12-3~ 12, 11, 10, 9
*Counting Up to Subtract
14-9~ 9… 10,11,12,13,14…answer is 5
*Doubles 7+7= 14 ~ Doubles Plus 1 7+8= 7+7+1
*Commutative Property 9+6= 6+9 9+6=15 so 6+9=15
*Relationship Between Addition and Subtraction 8+4=12 so 12-8+4
*Making 10 8+6= 8+2+4= 10+4= 14
*Decomposing a Number Leading to a Ten
13-4= 13-3-1= 10-1=9
9
Your child needs to memorize basic facts.
Lucy had 39 stickers and her mom gave her 24 more
stickers. How many stickers does Lucy have now?
(Solve and show your work)
10
. Traditional Algorithm is not taught until 3rd grade
Here are some common mistakes that students make,
and that test-makers take advantage of…
29 + 14
1
29 29 29
+14 +14 +14
43 313 16
(correct) (incorrect- failed to “carry the “one”
or added all the numbers together)
11
Direct Modeling
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Base 10
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100’s Chart
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Open Number Lines
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Number Strings
(Decomposing)
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Adding in Chunks
(Incrementing)
17
Compensation
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Subtraction
Lucy had 54 stickers and she gave her mom 29 of
them. How many stickers does Lucy have now?
*Students will often use related addition strategies when
solving subtraction strategies (29 + __ = 54)
19
common mistakes… 34-19= __
20
2 14
34 34
-19 -19
15 25
(correct) (incorrect- subtracted from the
bottom up in the ones place)
Direct Model
21
Base 10
22
Hundreds Chart
23
Open Number Line
24
Number Strings
(Decomposing) (leaving first number whole, decomposing second number)
25
Incrementing
26
Compensating
27
Sample 2nd grade test
question…
In the question, “There were 67 boys ad 54 girls
on the playground. How many kids were on the
playground?” a second grade student started
with 60 + 50 =110. What will they do next?
a. 60 + 4 c. 7 + 4= 11
b. 60 + 11 d. 50 + 7
28
Another Second grade
sample question…
29
Sample 3rd grade test
question…
Fill in the blanks below with whole numbers greater than 1 that will make
the number sentences true.
1. 63 ÷ ___ = 7
2. 63 = 21 × ___
3. 21 = ___ × 7
4. 7 × (___ × ___ ) = 21 × 7
5. (21 × 3) ÷ ___ = 7
Part B: If the product of two whole numbers greater than 1 is 63, what
could the two whole numbers be? _______, ________
30
Helping Your Child at Home
RELAX! Be Patient
*You are a “guide” - don’t take over for your child
*Believe that your child can be successful
*Expect your child to work hard to learn mathematics
*Always show all your work- have your child explain the problem
and his thinking out loud
*Talk about why solutions are correct and incorrect
*Help your child connect math with daily life
*Be supportive of methods your child shares from school
31
(feel free to e-mail your child’s teacher if you
have any questions)
32
Thank you for reading!!