P.S. 212-Grade K-2
Parent Math Workshop
January 31, 2014
What is it you want your children to learn
in Math?
We want your children to be problem solvers, to help them develop a
number sense and fluency.
What is a number sense?
Number Sense refers to a person’s understanding of number concept,
operations and applications of number and operations. It includes the
ability and inclination to use this understanding in flexible ways to
make mathematical judgments and to develop useful strategies for
handling numbers and operations. A person with good number sense
has the ability to use numbers and quantitative methods to
communicate, process, and interpret information.
Alistair McIntosh
Number Sense
 It builds capacity for doing mental math
 It involves the flexible decomposition of numbers (a very big
idea in mathematics!)
What is a number sense?
Please solve the following using multiple strategies:
387+ 464?
Fluency
 Having efficient and accurate methods for computing
 Flexibility in computational methods
 Understand and explain methods
 Produce accurate answers efficiently
 Understands base 10 number system
 Understands number relationships
 eg. What is the sum of 8+9=
Expectations for each grade according to
the Common Core Standards
 Kindergarten
 Decompose numbers less than or equal to 10 into parts in more than one way,
e.g., by using objects of drawings, and record each decomposition by a drawing
or equation (e.g., 5=2+3 and 5=4+1)
 Strategies
 • Organizing & keeping track
 • Counting all & Counting on
 • One-to-One Tagging: touch each object once and only once
 • Synchrony: one word for every object
 • Subitizing: identify quantities up to 5 without counting
Kindergarten Models
 • Fingers
 Ten Frame
 • Math Rack
What this looks like in Kindergarten
Example: Six crayons are in the box. Two are red and the rest
are blue. How many blue crayons are in the box?
Student: I got 6 crayons. I moved these two over and
pretended they were red. Then, I counted the “blue”
ones... 1, 2, 3, 4. Four. There are 4 blue crayons.
Expectations for each grade according to
the Common Core Standards

1st grade
 Use addition and subtraction within 20 to solve word
problems involving situations of adding to, taking from,
putting together, taking apart, and comparing, with
unknowns in all positions, e.g., by using objects, drawings,
and equations with a symbol for the unknown number
 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.
First Grade
 Big Ideas
 Understanding the relationship between addition and subtraction
 The commutative property
 Composing and decomposing of numbers
 Strategies
 Using the 5- and 10-structures (using the 10’s frame and/or the math
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rack)
Counting On
Skip Counting
Using Doubles and Near Doubles
Using Compensation
Making 10
What this looks like in first grade
42 cubes can be grouped many different ways and still remain a
total of 42 cubes.
4 tens and 2 ones
42 ones
2 tens and 22 ones
Expectations in each grade according to
the Common Core Standards
 2nd grade
 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.
 Use addition and subtraction within 100 to solve one- and two-step word
problems involving situations of adding to, taking from, putting together, taking
apart, and comparing, with unknowns in all positions, e.g., by using drawings
and equations with a symbol for the unknown number to represent the problem
 Students are expected to fluently add and subtract using the
standard algorithm by the end of grade 4
2nd Grade
 Big Ideas
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Equivalency 5 cent + 25 cent = 10c +10c +10c
Associative Property of Addition (9 + 3) + 7 = 9 + (3 + 7).
Expanded Form 19 + 21 = (10 + 9) + (20 + 1)
Subtraction as removal, difference, and used to find missing addends and subtrahends
Place Determines Value
Organize and represent mathematical thinking
 Strategies
 Counting On or Counting back
 Keeping one number whole
 Compensation, Regrouping
 Partial Sums
 Using Landmark or “friendly” numbers
 Using known addition and subtraction facts
What this looks like in second grade
Example: There were 17 students on the bus. Some more children got on. Then there were
32. How many came on? 17+?=32
Student A: I used a number line. I plotted the 17 and then I plotted the 32. The distance
between the two is the amount of children who got on the bus. I jumped 10 which
brought me to 27. I then jumped 3 more to bring me to a 10s number which is 30. I
then jumped 2 more to bring me to 32. I added up the total jumps which was 15. 15
children got on the bus.
Why use multiple strategies?
Addition Strategies
The following addition strategies reinforce and deepen place value understanding. They build
capacity for doing mental math, and they involve the flexible decomposition of numbers.
Split both numbers and add
57 + 28
50+20=70
7+8=15 (doubles +1)
70+14= 84
Keep one number whole and add
the other in parts
64 + 28 = 92
64+20=84
84+8=92
Use an “I know” fact
8+7=?
I know 7+7=14
so 7+8=15
compensation to solve an equivalent
49+51=(49+1) + (51-1)= 50+50
286 + 354 = (286 + 14) + (354 -14)= 300 + 340 = 640
A Number String in 1st Grade
 The number string routine
 How often do we do number strings?
 The expectations
 Student talk and ownership math
 An example… ( a string from last week)
Choose a strategy to solve:
 248+ 49
 114+44
 139+ 43
 39+38
 218+ 456
 387+ 464? (Would you do this differently now?)
Do students need to memorize math
facts?
YES!!!
 According to the common core standards by the end of second grade
students are expected to 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);
 Creating equivalent but easier or known sums (e.g., adding 6 + 7 by creating
the known equivalent 6 + 6 + 1 = 12 + 1 = 13).
 We begin to memorize math facts in Kindergarten
In Summary
 Each of the strategies taught allows students to make a
choice. When students consider the elements in a
problem and select a reasonably efficient strategy that
makes sense given the numbers or the context, they are
thinking like mathematicians.
 Mathematics is the study of relationships.
Seeing math as the study of relationships enables us to see structural
logic rather than just a series of random facts and procedures.
What can parents do at home?
 Have conversations that relate to everyday life and
incorporate math questions (eg. How tall is that tree?)
 Become familiar with the new math standards
 Practice counting objects and money
 Practice telling time everyday
 Reason through questions with your children.
 Play board games