elementary mathematics for iits @johnsangiovanni [email protected]
TRANSCRIPT
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.
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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
Formative Assessment is like
GPS.
1. Where are we going?2. Where are we?3. How are we getting there?
• 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.
• 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.
• 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.
• 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.
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?