Math Frameworks

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The mathematical processes – problem solving, communication, representations, reasoning and proof
and connections are the mathematical competencies that embody the “doing” of mathematics. These
processes should form the core of activities that students do and should provide focus and purpose for
the entire mathematics experience for students
NUMBER SENSE
UNDERSTAND THE BASE 10 NUMBER SYSTEM
Whole numbers
Understand relationships among numbers, including one to one
correspondence
Identify, write and order numbers 0-10,000 (<,>,=)
Identify and use place values from hundredths to ten thousands
Identify and write odd/even numbers
Use strategies for skip counting by 2s, 5s, 10s and 100s
Represent numbers, and equivalent forms of the same number, with
many different models including concrete objects
Decimals
Compare decimals values using tenths/hundredths as they relate to
cents
Write money values using decimals
Fractions - focus on student understanding of what a fraction represents
Write and use manipulatives to show fractions (halves, thirds, fourths)
Identify and explain the numerator and denominator as it relates to
parts of a whole or parts of a set
Order fractions (<,>,=)
Use fractions to represent quantities
Use drawings, models and diagrams to show the concept of fraction as part
of a whole
Show real world examples of fractional divisions (pizza, bookshelves, floor
tiles, etc.)
Key:
UNDERSTAND THE RELATION SHIP BETWEEN ADDITION AND SUBTRACTION
Understand the process
Understand various meanings of addition and subtraction
Understand addition and subtraction as inverses of each other
Understand addition as:
combining sets
increasing an amount
comparing two sets
equalizing groups (missing addends)
Understand subtraction as:
separating sets
taking away from a set
comparing sets and finding the difference
Problem solving
Use estimation/rounding to verify answer
Use properties to solve problems (commutative, associative)
Use mental math strategies
Use different strategies to solve addition/subtraction problems
Analyze the problem to identify the correct operation
Bold = Mastery
Italics = Introduce
Regular font – Teach and practice
rd
3 Grade
The mathematical processes – problem solving, communication, representations, reasoning and proof
and connections are the mathematical competencies that embody the “doing” of mathematics. These
processes should form the core of activities that students do and should provide focus and purpose for
the entire mathematics experience for students
Apply and explain multi-digit addition and subtraction algorithms
Fluency
REVIEW: Addition/Subtraction facts to 20
Add numbers up to 4 digits
Subtract whole numbers with 3 digits or less with and without
regrouping
Add and subtract money/make change
Add/subtract fractions with like denominators
Add/subtract decimals related to money
UNDERSTAND MULTIPLICATION AND DIVISION WITHIN 100
Understand the process
Understand multiplication as:
repeated addition
combining equal groups
using arrays
area models
linear models
Cartesian models
Understand division as:
repeated subtraction
finding equal shares
Understand the relationship between multiplication and division
Understand Problem Solving
Represent multiplication and division problems using different models
Use different strategies to solve multiplication and division facts and
problems including multi-step problems and determine reasonableness of
answers
Analyze the problem to identify the correct operation
Solve single digit multiplication problems using a variety of strategies
Fluency
MASTER: Multiplication facts 10x10
Division facts 10 x 10
Use multiplication facts to solve division facts division as repeated
subtraction, finding equal shares
Solve single digit multiplication problems using a variety of strategies
VOCABULARY:
Relative, magnitude, equivalence, whole numbers, expanded form, fraction, place value, estimate,
subtraction, skip count, odd, even division, multiplication, decimal, product, factor, numerator,
denominator, quotient, addend, commutative, associative, identify property, multiples, base 10
system, zero property, digit, tens, thousands, greater than, less than, addition, fact family, problem,
sum, all together, total, difference, equal
Key:
Bold = Mastery
Italics = Introduce
3rd Grade
Regular font – Teach and practice
The mathematical processes – problem solving, communication, representations, reasoning and proof
and connections are the mathematical competencies that embody the “doing” of mathematics. These
processes should form the core of activities that students do and should provide focus and purpose for
the entire mathematics experience for students
GEOMETRY
GEOMETRIC ELEMENTS
Represent and use terms and concepts of: angles vertex, face, edge and sides, bases,
vertices
ANALYZE CHARACTERISTICS AND PROPERTIES OF 2 DIMENSIONAL SHAPES
Name, describe attributes and provide examples: circles, triangles, squares,
rectangles, trapezoids, rhombuses, pentagons, hexagons
Identify 2D shapes when turned, flipped or slide
ANALYZE CHARACTERISTICS AND PROPERTIES OF 3 DIMENSIONAL SHAPES
Name, describe attributes and provide examples of 3D shapes: spheres, cones,
cylinders, pyramids, cubes
COORDINATE GRAPHING
Locate points on a grid representing a positive coordinate system
IDENTIFY AND DESCRIBE SYMMETRY
Describe and provide examples of lines of symmetry
Vocabulary: edges, sides, corners, faces, vertices, angles, hexagon, cones, cylinders, pyramids,
cubes, sides, corner, trapezoid, symmetry, points, grid, coordinate system, ordered pairs, bases,
circle, triangle, square, rectangle, rhombus, two-dimensional, three dimensional, geometric
elements, flips, sides, turns, sort, classify, edges, vertex, attribute, reflections (flips), translations
(slides), rotations (turns)
MEASUREMENT
UNDERSTAND MEASURABLE ATTRIBUTES
Apply understanding of measurement
Measurement is used to describe attributes of objects.
Different measurement systems are used to measure different attributes
(length, weight, etc.)
Measurement systems are predictable once you understand how it is
organized.
Apply understanding of length
Measure objects to nearest ½ inch or nearest centimeter
Use a ruler to measure length
Choose and use appropriate tool
Describe and compare and order objects on the basis of length
(longer/shorter)
Estimate length
Convert units for length (inch, foot).
Apply understanding of weight
Weigh objects to the nearest pound (oz, pound)
Use a scale or balance
Describe and compare attributes of an object using weight.
Estimate weight
Convert units for weight (ounce, pound)
Apply understanding of time
Key: Bold = Mastery
Italics = Introduce
Regular font – Teach and practice
rd
3 Grade
The mathematical processes – problem solving, communication, representations, reasoning and proof
and connections are the mathematical competencies that embody the “doing” of mathematics. These
processes should form the core of activities that students do and should provide focus and purpose for
the entire mathematics experience for students
Identify parts of a clock
Measure time (hours, half-hours, quarter hours, five and one minute
intervals
Use a clock
Estimate time
Convert units for time (minutes, hours, days, weeks, months)
Determine elapsed time by half hours
Apply understanding of money
Identify coins and bills by value
Use coins and bill to count to $5.00
Identify, compare and order amounts of money using coins and bills
Use correct symbols for money
Combine coins and bills to make a given amount
Estimate cost
Convert units within the same measurement system including money
(dollars, cents)
Apply understanding of temperature
Measure temperature using Fahrenheit and Celsius to the nearest degree
Use a thermometer
Describe attributes of an object using temperature
Estimate temperature
Vocabulary: standard, nonstandard, inch, foot, centimeter, length, weight, unit, Fahrenheit, Celsius,
thermometer, weight, measure, length, coin, bill, hour, half hour, quarter hour, ruler, o’clock, hour,
half hour, meter, yard, ounce, gram, perimeter, elapsed time, dollar, penny, nickel, dime, quarter
At 3rd Grade teach time and money during math time, teach measurement of length, weight
and temperature in Science.
ALGEBRA
UNDERSTAND PATTERNS, RELATIONS, AND FUNCTIONS
Extend patterns (numbers, pictures, words)
Describe functions (input-output) through pictures and words
Describe and explain a pattern
Demonstrate simple function rules
EXPLORE UNKNOWNS AND OPEN SENTENCES TO EXPRESS RELATIONSHIP
Solve simple addition and subtraction equations with missing values
Model real world and mathematical problems with simple number sentences
Determine the value of an output given as a function rule and an input value
Vocabulary: patterns, functions, input, output, function rules, open sentences, unknowns,
equations, missing values
Key: Bold = Mastery
Italics = Introduce
Regular font – Teach and practice
rd
3 Grade
The mathematical processes – problem solving, communication, representations, reasoning and proof
and connections are the mathematical competencies that embody the “doing” of mathematics. These
processes should form the core of activities that students do and should provide focus and purpose for
the entire mathematics experience for students
DATA AND PROBABILITY
Graphs should be used across the curriculum
USE, ORGANIZE AND DISPLAY DATA
Read and interpret drawings, tables/charts, tally tables, pictographs, bar
graphs circle graphs with 2 or 3 sectors, line plots, 2 circle Venn diagram
Analyze and make inferences from the data
Make predictions
Describe data using mode and range of a set of data
Identify cause/effect relationships
Draw simple conclusions
Form and justify an opinion on whether a given statement is reasonable based
on the analyzed data
Identify the specific purpose of various graphs
Bar graph: compare data
Pictograph: compare data using pictures
Tables/charts: organize data
Circle graph: shows parts of a whole
Choose the appropriate graph to use based on the data: bar graph, circle graph and
pictograph
Use data to answer questions:
Ask a question with a quantifiable answer
Collect data
Organize and display data using bar graphs, pictographs, venn diagrams,
tables/charts
Use parts of a graph: labels, appropriate scale, title, x & y axis
APPLY BASIC CONCEPTS OF PROBABILITY
Describe and give examples of the probability of an unlikely event and a likely event
Use simple experiments to explore probability
Determine if events are probable or improbable
Vocabulary: graph, tally tables, pictograph, bar graph, circle graph, venn diagram, line plot, likely,
unlikely, probability, chance, inferences, drawings, tables, charts, data display, sector, mode, range,
display, conclusion
Key:
Bold = Mastery
Italics = Introduce
3rd Grade
Regular font – Teach and practice
The mathematical processes – problem solving, communication, representations, reasoning and proof
and connections are the mathematical competencies that embody the “doing” of mathematics. These
processes should form the core of activities that students do and should provide focus and purpose for
the entire mathematics experience for students
Key:
Bold = Mastery
Italics = Introduce
3rd Grade
Regular font – Teach and practice
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