Elementary Mathematics For IITs jsangiovanni@hcpss.org @JohnSanGiovanni

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? Very Important Somewhat Important Less Important

Kindergarten *Important: Somewhat 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. 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: Somewhat 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. Represent and interpret data. Less important: Tell and write time. Reason with shapes and their attributes.

Second Grade *Important: Somewhat 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. 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: Somewhat 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. 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: Somewhat Important: Less 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. 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: Somewhat 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. 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.

How should instruction and assessment be related? 1 2 I I A A 3 4 I A A I

Extended response tasks Selected Response Items Observations Interviews Conversations Extended response tasks Journals and reflections Open-Ended Questions Exit tickets Reports and projects Portfolios

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. Where are we going? Where are we? How are we getting there? jsangiovanni@hcpss.org

Formative Assessment is like GPS. • 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? jsangiovanni@hcpss.org

Formative Assessment is like GPS. • 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? jsangiovanni@hcpss.org

Formative Assessment is like GPS. • 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? jsangiovanni@hcpss.org

Formative Assessment is like GPS. • 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? 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? Where are we? 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)

How would we assess these students?

What Do We Do When They Don’t Get It What Do We Do When They Don’t Get It? Progression of Skills Within a Standard Rote Counting Counting objects Read/write How will we get there? 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)

http://grade3commoncoremath.wikispaces.hcpss.org

Assessment Tasks by Standard Additional Problem Solving Tasks Number Readiness Assessments http://grade3commoncoremath.wikispaces.hcpss.org

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 Ideas **Go to Math WIKI** Ask teacher for Teaching Student Centered Mathematics Check out the Math Weebly at: http://hcpssfamilymath.weebly.com/ Consider: “Exposure, Practice, Conversation” More on the way Summer 2015!

What is something from today that resonates with you?