Mathematics

Grade 6

Use alternative forms of expressing rational numbers

Initial Understanding

Rename equivalent fractions and mixed numbers.

Rename equivalent fractions and mixed numbers as equivalent decimals, and vice versa

Developing an Interpretation

Identify alternative forms of expressing whole numbers < 100,000 using expanded notation and regrouping

Making Connections

Solve problems involving 100, 1000, 10,000 more or less and 0.1 more or less than a number

Use Integers, decimals and fractions to; determine magnitude, compare, order, picture and round

Initial Understanding

Locate points on number lines and scales, including fractions decimals and integers.

Construct pictorial representations of decimals (tenths & hundredths) and mixed numbers

Construct fractions mixed number’s, decimals percents to their pictorial representations and vice versa

Developing an Interpretation

Order and describe the magnitude of whole numbers and decimals (tenths and hundredths)

Order fractions and mixed number

Describe the magnitude of whole numbers and decimals (tenths and hundredths)

Describe the magnitude of fractions and mixed numbers.

Making Connections

Round whole numbers and fractions and decimals in a context

Develop estimation strategies

Developing an Interpretation

Identify the best expression. To find an estimate.

Identify whether and why a particular strategy will result in an overestimate or an underestimate.

Identify the best expression to find an estimate

Estimate length, areas and angle measurement

Identify whether and why a particular strategy will result in an overestimate or an underestimate

Making Connections

Estimate length, areas and angle measurement

Determine a reasonable estimate and describe the strategy used to make the estimate.

Critical Stance

Estimate a reasonable answer to a problem and make and defend decision

Use strategies, to add and subtract, multiply, and divide rational numbers.

Initial Understanding

Add and subtract fractions and mixed numbers with reasonable and appropriate denominators

Multiply whole numbers and fractions by fractions and mixed numbers.

Add and subtract 2-, 3-, and 4- digit whole and decimals

Multiply and divide whole numbers by 10, 100 and 1000.

Multiply and divide 2- and 3- digit whole numbers and money amounts by 1- digit numbers and decimals.

Developing an Interpretation

Identify the correct placement of the decimal point in multiplication, and division of decimals by one digit numbers.

Identify or write the appropriate operation or # sentence to solve a story problem

Making Connections

Solve 1-step problems involving fraction decimals and money

Solve 2-step problems involving whole number’s fractions, decimals mix number’s, including averaging

Solve 2-step problems involving whole numbers, decimal fractions and mixed numbers, with extraneous information.

Solve 2-step problems and explain how the solution was determined.

Write story problems from equations involving fractions and decimals.

Solve problems involving ratios

Solve extended numerical problems

Develop Algebraic Concepts

Initial Understanding

Solve 1-step algebraic equations

Evaluate expression and use formulas

Developing an Interpretation

Identify or state rules for given pattern

Making Connections

Extend or complete patterns involving whole number’s and attributes,

Critical Stance

State and defend the rule or equation for patterns involving whole numbers. And attributes

Use Elementary Statistics and Probability to analyze Data

Initial Understanding

Create bar and line graphs from data in tables and charts

Developing an Interpretation

Identify correct information from graphs, tables, and charts

Making Connections

Solve extended statistical problems

Solve problems involving elementary notions of probability. and fairness, include justifying answers

Draw and justify reasonable conclusions from graphs, tables, and charts

Solve problems involving means and medians of set of data

Solve problems involving organization of data including sorting objects by common attributes

Apply time, measure length, find area and volume

Initial Understanding

Measure or determine perimeter and area, volume

Developing an Interpretation

Identify appropriate customary or metric units of measure for a given situation

Making Connections

Solve problems involving the conversion of units of measures including time

Develop spatial relationships in Plane Geometry

Initial Understanding

Draw geometric shapes and figures

Describe and classify geometric shapes and figures

Developing an Interpretation

Identify and draw lines of symmetry

Identify geometric transformations

Identify congruent & similar figures

Identify points on a grid

Making Connections

Solve extended spatial problems

Critical Stance

In Mathematics justifying, proving or explaining a conjecture or answer is connected to the learning environment. Students are encouraged and expected to question one an others’ ideas and to explain and support their own ideas in the face of others’ challenges. Each objective in mathematics can be framed to have students defend support, explain or prove their answer. Educational research offers compelling evidence that student learn mathematics well only when they construct their own mathematical understandings. To understand what they learn, students must enact for themselves verbs that permeate the mathematics curriculum: “examine”, “represent”, ”transform”, “solve”, “apply”, “prove”.

Mathematics

GRADE 6

EXPAND CORE

Develop number and number relationships with integers, rational and irrational numbers

Use computation and estimation strategies with rational numbers and integers

Use strategies, to solve problems with numbers and variables

Develop Algebraic Concepts

Use Elementary Statistics and Probability to analyze Data

Explore Geometry and measurement in two and three dimensions

Mathematics

GRADE 6

EXPANDED CORE

Develop number and number relationships with integers, rational and irrational numbers

Initial Understanding

Order whole number’s, and decimals.

Round whole numbers decimals.

Developing an Interpretation

Identify alternative forms of expressing #'s expanded notation.

Identify alternative forms of expressing #'s, using scientific notation

Relate fractions, decimals, and percents to pictorial presentations & vice versa.

Construct pictorial representations of fractions, decimals, and percents

Rename equivalent fractions & mixed #'s as equivalent decimals & vice versa.

Rename fractions & decimals as equivalent percents & vice versa or state rules for given pattern

Order fractions mixed numbers

Describe magnitude of whole #’s and decimal

Describe magnitude of fractions or mixed number’s

Round whole numbers, fractions and decimals in context

Making Connections

Describe magnitude whole numbers in context.

Locate points on # lines/scales, including fractions, decimals, & integers.

Use computation and estimation strategies with rational numbers and integers

Initial Understanding

Add and -Subtract 2, 3, 4-digit whole #'s, & decimals

Multiply &. Divide whole #'s, decimal [10, 100 1000].

Multiply & divide 2, 3-digit whole. #’S, $, decimal. By 1 digit #'s, & decimal

Add & subtract fraction, mixed #'s with reasonable and appropriate denominators.

Developing an Interpretation

Identify best expression to find estimate

Find percents of whole #'s or

Identify whether & why a particular strategy will result in over or underestimate

Find percents of whole #'s or the percent a given # is of another #.

Making Connections

Estimate a reasonable answer to a problem

Multiply whole #'s & fractions by fractions and mixed numbers.

Solve 1-step problems involving fractions and mixed #'s.

Solve multi-step problems: whole #'s, decimals, fractions, and mixed #’s including averaging.

Solve problems involving whole #'s, decimal, fractions, mixed #'s with extraneous. Information

Solve multi-step problems; justify solutions.

Solve problems involving ratios

Solve problems involving proportions

Solve problems involving percent

Critical Stance

Explain and defend why estimate is or is not reasonable.

Estimate to make or defend a decision.

Use strategies, to solve problems with numbers and variables

Developing an Interpretation

Identify appropriate operations or # sentences to solve story problems.

Making Connections

Solve 1-step probe: whole. #’S, decimals, $.

Solve multi-step problems; justify solution.

Solve multi-step problems involving whole numbers

Solve problems involving: 0.1/0.01 .001 more/less.

Write story problems from equations involving rational numbers, integers and variables

Solve extend numerical problems

Develop Algebraic Concepts

Initial Understanding

Solve simple 1 -step equations.

Use order of operations

Evaluate expressions & use formulas.

Developing an Interpretation

Write expressions to represent a given situation.

Identify or extend patterns involving #'s and attributes

Identify or state rules for given patterns, write the formula

Identify points on grids.

Making Connections

Represent situations with algebra expression.

Use Elementary Statistics and Probability to analyze Data

Initial Understanding

Organize data.

Create graphs from data: tables and charts.

Developing an Interpretation

Identify correct information: graphs, tables, and charts.

Making Connections

Draw reasonable conclusions from graphs, tables, and charts.

Solve problems involving means and medians of sets of data.

Solve extend and statistical problems

Solve problems. Involving organization of data.

Solve problems involving elementary notions of probability, fairness, including justifying answers

Solve problems involving expected outcomes or predictions.

Critical Stance

Justify reasonable conclusions from graphs, tables, and charts.

Explore Geometry and measurement in two and three dimensions

Initial Understanding

Draw geometry shapes and figures.

Describe, model, and classify shapes.

Measure and determine perimeter, area, and volume.

Developing an Interpretation

Estimate lengths, area, and angle measurement.

Identify or draw geometry transformations.

Identify draw and describe lines of symmetry.

Identify appropriate customary or metric measure for a given situation.

Relate 2-dimensional and 3-dimensional. Representations

Identify or describe congruent and similar figures.

Identify points on grids.

Making Connections

Solve problems involving conversions of units of measure, including time.

Solve extend spatial problems

Critical Stance

In Mathematics justifying, proving or explaining a conjecture or answer is connected to the learning

environment. Students are encouraged and expected to question one an others’ ideas and to explain and

support their own ideas in the face of others’ challenges. Each objective in mathematics can be framed to have

students defend support, explain or prove their answer. Educational research offers compelling evidence that

student learn mathematics well only when they construct their own mathematical understandings. To

understand what they learn, students must enact for themselves verbs that permeate the mathematics

curriculum: “examine”, “represent”, ”transform”, “solve”, “apply”, “prove”.