Math Morning
Third Grade 10/30/13
Welcome to Math Morning, the third grade edition!
 Agenda
 Provide a sense of how we teach math
 Quick sample of one of the kids’ daily math routines
 What is TERC Investigations? What is EngageNY?
 Offer insight into the Common Core State Standards for third grade
 Guide you through a sample math workshop
 Give some guidance about how best to help your child with his/her math work at home
How We Teach Math: Daily Routines
 Emphasize math routines that build an understanding of the composition of
numbers
 Number of the Day routine
 Find the ways to make equal groups with 36
 Share thinking with the group
 Enables kids to see how others thought about the problem
 Requires kids to verbalize their math thinking
 Deepens understanding by way of teaching
How We Teach Math: Daily Routines
 Purpose of this daily routine
How We Teach Math: Daily Routines
 Kids develop an understanding that numbers have parts
 They’re literally building and taking apart numbers
How We Teach Math: Daily Routines
 Enables various access points to the same material
 Struggling kids are always able to see equal groups of 1 or 1 large group of __
 Higher kids can start to think about fractions (e.g. how many 1/2s are in 36? 1/4s?)
How We Teach Math: Daily Routines
 Fosters awareness of repetition within our number system
 e.g. all even numbers can be split into two equal groups
How We Teach Math: Daily Routines
 Pushes kids’ understanding of factors, multiples, and the relationship between
multiplication and division
How We Teach Math: TERC Investigations
 Constructivist approach
 Support students as they make sense of math and learn that they can be mathematical
thinkers
 Emphasis is not on one teacher-directed strategy or algorithm that students must then
adopt
 “Investigations takes seriously the time students need to develop a strong conceptual
foundation and skills based on that foundation.” (investigations.terc.edu)
 This approach is essential for building confidence, flexibility, and conceptual
understanding
 Kids will see algorithms in later years; must have conceptual foundation in order to
understand these more traditional methods
How We Teach Math: EngageNY
 Created by NYSED in response to new Common Core State Standards
 More focus on direct instruction with student practice
 Emphasis on fluency with basic facts and core skills
Common Core State Standards (CCSS)
Common Core State Standards (CCSS)
 Not a panic-button situation at PS 29
 TERC released CCSS-aligned supplemental materials more than two years ago
 Teachers have been working with staff developers and each other to revamp
units and ratchet up curriculum within and across grades for more than two
years
 The fuss about rigor
 Third-grade standards are more demanding
 We’ve been preparing the kids for that shift across grades
The actual standards
Common Core State Standards (CCSS)
 Operations and Algebraic Thinking
 Represent and solve problems involving multiplication and division
 Understand properties of multiplication and the relationship between multiplication and division
 Multiply and divide within 100
 Solve problems involving the four operations, and identify and explain patterns in arithmetic
 Number and Operations in Base Ten
 Use place value understanding and properties of operations to perform multi-digit arithmetic
 Number and Operations – Fractions
 Develop understanding of fractions as numbers
 Measurement and Data
 Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects
 Represent and interpret data.
 Geometric measurement: understand concepts of area and relate area to multiplication and to addition
 Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures
 Geometry
 Reason with shapes and their attributes
Common Core State Standards (CCSS)
Full content of the standards
 http://www.corestandards.org/Math/Content/3/introduction
 Use navigational links on the left of the screen
Standards unpacked with examples and explanations
 http://www.ncpublicschools.org/docs/acre/standards/common-core-tools/unpacking/math/3rd.pdf
Standards and New York curriculum
 http://www.engageny.org/
Sample Math Workshop
 Remember the work we did earlier?
 Equal groups with 36
 Time to bake some factor cake
 Helps us to see all the ways to divide 36 into equal groups
 Each layer of cake shows a different way to divide 36 into equal groups
 Let’s do a few layers together
Sample Math Workshop
 Factor Cake for 36
36
Sample Math Workshop
36
18
18
12
12
9
9
6
4
4
1
1
2
1
1
3
2
1
6
4
3
2
9
6
3
12
1
2
1
1
2
1
1
4
3
2
1
6
4
3
1
1
1
2
1
1
3
2
1
6
4
3
2
9
1
2
1
1
4
3
2
1
4
3
2
1
6
1
3
2
1
1
4
2
1
1
3
2
1
1
3
2
1
1
2
1
1
2
1
1
1
Sample Math Workshop
 I have 12 bags. There are 3 apples in each bag. How many apples do I have in
all?
 Which layer of factor cake helps you to see this story problem?
 The work’s already been done! How can we write an equation to represent this
story problem?
Sample Math Workshop
 I have 12 bags. There are 3 apples in each bag. How many apples do I have in
all?
 Which layer of factor cake helps you to see this story problem?
 The work’s already been done! How can we write an equation to represent this
story problem?
36
18
18
12
12
9
9
6
4
4
1
1
2
1
1
3
2
1
6
4
3
2
9
6
3
12
1
2
1
1
2
1
1
4
3
2
1
6
4
3
1
1
1
2
1
1
3
2
1
6
4
3
2
9
1
2
1
1
4
3
2
1
4
3
2
1
6
1
3
2
1
1
4
2
1
1
3
2
1
1
3
2
1
1
2
1
1
2
1
1
1
Sample Math Workshop
 I have 12 bags. There are 3 apples in each bag. How many apples do I have in
all?
 Which layer of factor cake helps you to see this story problem?
 The work’s already been done! How can we write an equation to represent this
story problem?
 12 x 3 = ?
 12 x 3 = 36
Sample Math Workshop
 There are 36 markers packed 4 to a box. How many boxes are needed to hold
all the markers?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
Sample Math Workshop
 There are 36 markers packed 4 to a box. How many boxes are needed to hold
all the markers?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
36
18
18
12
12
9
9
6
4
4
1
1
2
1
1
3
2
1
6
4
3
2
9
6
3
12
1
2
1
1
2
1
1
4
3
2
1
6
4
3
1
1
1
2
1
1
3
2
1
6
4
3
2
9
1
2
1
1
4
3
2
1
4
3
2
1
6
1
3
2
1
1
4
2
1
1
3
2
1
1
3
2
1
1
2
1
1
2
1
1
1
Sample Math Workshop
 There are 36 markers packed 4 to a box. How many boxes are needed to hold
all the markers?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
 36÷ ? = 4
 36÷9 = 4
Sample Math Workshop
 You have 36 inches of string which you will cut into 6 equal pieces. How long
will each piece of string be?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
Sample Math Workshop
 You have 36 inches of string which you will cut into 6 equal pieces. How long
will each piece of string be?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
36
18
18
12
12
9
9
6
4
4
1
1
2
1
1
3
2
1
6
4
3
2
9
6
3
12
1
2
1
1
2
1
1
4
3
2
1
6
4
3
1
1
1
2
1
1
3
2
1
6
4
3
2
9
1
2
1
1
4
3
2
1
4
3
2
1
6
1
3
2
1
1
4
2
1
1
3
2
1
1
3
2
1
1
2
1
1
2
1
1
1
Sample Math Workshop
 You have 36 inches of string which you will cut into 6 equal pieces. How long
will each piece of string be?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
 36÷6 = ?
 36÷6 = 6
Sample Math Workshop
 I have 12 bags. There are 3 apples in each bag. How many apples do I have in
all?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
 There are 36 markers packed 4 to a box. How many boxes are needed to hold
all the markers?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
 You have 36 inches of string. You cut the string into 6 equal pieces. How long
is each piece of string?
 Which layer of factor cake helps you to see this story problem?
 How can we write an equation to represent this story problem?
Sample Math Workshop
 Unpacking the activity
 Deepening an understanding of the relationship between multiplication and division
 Allowing multiple access points for different learners
 Developing fluency with factors of 36
How You Can Support Your Child’s Math Work
 Recognize that developing a deep understanding of the concepts we are studying takes time, and each child develops at his/her own pace
 Help your child persevere when a problem is challenging. Some questions you can ask:
 Have you ever seen a problem like this before? What do you think the problem is asking you to do?
 What information do you have? What information are you missing?
 Can you make a model, a picture, a diagram, or an equation to help you understand what is happening in the problem?
 What tools and strategies do you already know that could help you with this?
 Share your own mathematical methods with your child, but also allow him/her to share his/her methods; help make connections between
the two approaches
 Encourage your child to give homework his/her best effort, but recognize when your child has reached his/her limit. Fifteen minutes of
solid, independent work-time is a good guideline!
 If your child is looking for a challenge, feel free to create problems based on the homework problems, or check engageny.org for more
ideas. Additionally, kids know how to ratchet up the level of difficulty on problems like those given in class
How You Can Support Your Child’s Math Work
(continued)
 Encourage speed and automaticity with basic facts (addition, subtraction, and multiplication)
 Practice telling time
 Work with money and ask your child to make change