Elementary Mathematics For IITs @JohnSanGiovanni jsangiovanni@hcpss.org

Elementary Mathematics

For IITs

@JohnSanGiovanni

jsangiovanni@hcpss.org

Objectives…

• Enhance our understanding of what is important in elementary mathematics

• Identify how we can gather information about concerns in elementary mathematics

• Identify intervention resources

How do you define “number sense?”

Number Sense is…

Number Sense

• “a well organized conceptual framework of number information that enables a person to understand numbers and number relationships and to solve mathematical problems that are not bound by traditional algorithms" (Bobis, 1996).

Number Sense

• An intuitive understanding of numbers, their magnitude, relationships, and how they are affected by operations.

-Learn NC, University of North Carolina

Number Context and Number Sense

What math content is most important?

o Very Important o Somewhat Importanto Less Important

Kindergarten

*Important:• Know number names and

count sequence.• Count to tell the number of

objects. • Compare numbers.• Understand addition and

subtraction. • Work with numbers 11-19

to gain foundations for place value.

Somewhat Important: • Analyze, compare, create

and compose shapes. • Classify objects and count

the number of objects in categories.

Less important:• Identify and describe

shapes.• Describe and compare

measurable attributes.

First Grade

*Important:• Represent and solve problems

involving addition and subtraction.• Understand and apply properties of

operations and the relationship between addition and subtraction.

• Add and subtract within 20.• Work with addition and subtraction

equations. • Extend the counting sequence. • Understand place value.• Use place value understanding and

properties of operations to add and subtract.

• Measure lengths indirectly and be iterating length units.

Somewhat Important: • Represent and interpret

data.

Less important:• Tell and write time.• Reason with shapes and

their attributes.

Second Grade

*Important:• Represent and solve problems

involving addition and subtraction.

• Add and subtract within 20.• Understand place value.• Use place value understanding

and properties of operations to add and subtract.

• Measure and estimate lengths in standard units.

• Relate addition and subtraction to length.

Somewhat Important: • Work with equal groups of

objects to gain foundations for multiplication.

• Work with time and money.• Represent and interpret

data.

Less important:• Reason with shapes and

their attributes.

Third Grade

*Important:• 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.

• Develop understanding of fractions as numbers.

• Solve problems involving measurement and estimation of intervals of time, liquid volumes and masses of objects.

• Understand concepts of area and relate area to multiplication and addition.

Somewhat Important: • Represent and interpret

data.• Reason with shapes and

their attributes.

Less important:• Recognize perimeter as an

attribute of plane figures and distinguish between linear and area measures.

Fourth Grade

*Important:• Use the four operations with whole

numbers to solve problems.• Generalize place value understanding

for multi-digit whole numbers.• Use place value understanding and

properties of operations to perform multi-digit arithmetic.

• Extend understanding of fraction equivalence and ordering.

• Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.

• Understand decimal notation for fractions, and compare decimal fractions.

Somewhat Important: • Gain familiarity with factors and

multiples. • Solve problems involving

measurement and conversion of measurements from a larger until to a smaller unit.

• Represent and interpret data.

Less important:• Understand concepts of angle and

measure angles. • Draw and identify lines and angles,

and classify shapes by properties of their lines and angles.

Fifth Grade

*Important:• Understand the place value system.• Perform operations with multi-digit

whole numbers and with decimals to hundredths.

• Use equivalent fractions as a strategy to add and subtract fractions.

• Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

• Understand concepts of volume and relate volume to multiplication and to addition.

Somewhat Important: • Convert like measurement units

within a given measurement system.• Represent and interpret data.

Less important:• Write and interpret numerical

expressions. • Analyze patterns and relationships. • Graph points on the coordinate plane

to solve real-world and mathematical problems.

• Classify two-dimensional figures into categories based on their properties.

I I

I I

A A

A A

12

3 4

INSTRUCTION ASSESSMENT

How should instruction and assessment be related?

Observations

Interviews

Conversations

Extended response tasks

Journals and reflections

Open-Ended Questions

Exit ticketsReports and projects

Portfolios

Selected Response Items

Successful Formative Assessment

• Know what we’re looking for

• Consider “levels” of what we’re looking for

• Record/communicate what we find

• Use the results to make instructional decisions

jsangiovanni@hcpss.org

Formative Assessment is like

GPS.

1. Where are we going?2. Where are we?3. How are we getting there?

jsangiovanni@hcpss.org

• Understand the Standard – What does proficiency look like?• What skills are “prerequisites” for success?• What do they understand in this progression?• How will we move forward?

Formative Assessment is like

GPS.

jsangiovanni@hcpss.org

• Understand the Standard – What does proficiency look like?• What skills are “prerequisites” for success?• What do they understand in this progression?• How will we move forward?

Formative Assessment is like

GPS.

jsangiovanni@hcpss.org

• Understand the Standard – What does proficiency look like?• What skills are “prerequisites” for success?• What do they understand in this progression?• How will we move forward?

Formative Assessment is like

GPS.

jsangiovanni@hcpss.org

• Understand the Standard – What does proficiency look like?• What skills are “prerequisites” for success?• What do they understand in this progression?• How will we move forward?

Formative Assessment is like

GPS.

jsangiovanni@hcpss.org

The Standard

• Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. (1.NBT.1)

Where are we going?

What would you look for as students complete this task?

Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. (1.NBT.1)

Where are we?

How would we assess these students?

What Do We Do When They Don’t Get It?Progression of Skills Within a Standard

Count to 120, starting at any number less than 120. In this range, read and write numerals and represent a number of objects with a written numeral. (1.NBT.1)

Rote Counting

Counting objects

Read/write

How will we get there?

http://grade3commoncoremath.wikispaces.hcpss.org

http://grade3commoncoremath.wikispaces.hcpss.org

Assessment Tasks by Standard

Additional Problem Solving Tasks

Number Readiness Assessments

Formative Assessment

• Student learning targets• Formative assessment

tasks• Systemic rubric• Progression of skills and

concepts

Need more information?

Try the number readiness assessment at that grade level or the grade level

below.

Where to go for Intervention Ideas1. **Go to Math WIKI**

2. Ask teacher for Teaching Student Centered Mathematics

3. Check out the Math Weebly at:

http://hcpssfamilymath.weebly.com/

4. Consider: “Exposure, Practice, Conversation”

More on the way Summer 2015!

What is something from today that resonates with you?