Math Unit 1 Overview MATH Grade 6 Unit 1 : Rates, Ratios and Proportions Time Frame: 21 days Key Vocabulary: column, row, factor puzzle, factors, product, multiple, rate table, unit rate, ratio, rate, constant rate, unit rate, every, each, per, scrambled rate table, unit price, coordinate plane, x-axis, y-axis, ordered pair, coordinates, x- coordinate, y-coordinate, unit rate triangle, speed, distance, time, linked rate table ratio table, basic ratio, equivalent ratios, proportion, solving a proportion, , greatest common factor, scale Essential Questions: What is ratio and ratio reasoning? How does a ratio help us to compare quantities? How does multiplication and division help us to understand ratios concepts and apply it to problem solving? Big Ideas: Multiplication and Rates Special Rate Situations and Graphing Solve Problems with Ratio and Proportion Identify, Solve and Write proportion Situations Suggested Mentor Texts: N/A Technology: Destination Math Mega Math Soar to Success Interactive iTools
29
Embed
Unit 1 : Rates, Ratios and · PDF fileUnit 1 : Rates, Ratios and Proportions Time Frame: 21 days ... CC.K-12.MP.1 Make sense of problems and ... Form A pre-test Formative
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
Math Unit 1 Overview
MATH
Grade 6
Unit 1 : Rates, Ratios and Proportions
Time Frame: 21 days
Key Vocabulary: column, row, factor puzzle,
factors, product, multiple, rate table, unit rate,
ratio, rate, constant rate, unit rate, every, each,
How does multiplication and division help us to understand ratios concepts and apply it to
problem solving?
Big Ideas:
Multiplication and Rates
Special Rate Situations and Graphing
Solve Problems with Ratio and Proportion
Identify, Solve and Write proportion Situations
Suggested Mentor Texts:
N/A
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.EE.5 Understand solving an equation or inequality as a process of answering a question: which values from a specified set, if any, make the equation or inequality true? Use substitution to determine whether a given number in a specified set makes an equation or inequality true.
6.EE.9 Use variables to represent two quantities in a real-world problem that change in relationship to one another; write an equation to express one quantity, thought of as the dependent variable, in terms of the other quantity, thought of as the independent variable. Analyze the relationship between the dependent and independent variables using graphs and tables, and relate these to the equation.
Mathematical Practices
CC.K-12.MP.1 Make sense of problems and
Relate factor puzzles to four numbers in the multiplication table
Learn strategies for solving factor puzzles
Learn a quick practice routine
Solve and make factor puzzles
Understand rate situations as involving a constant increase
Distinguish multiplication situations from non-multiplication
situations
Make a table to show a rate situation for many multiples of the
situation
Understand rate tales as columns of the multiplication table
Understand unit rate and totals made from rates
Understand unit rate language
Understand how a rate table is related to equal-groups
multiplication
Decide if a constant rate is reasonable for a given situation
Identify rate tables and make up rate situations
Find the unit rate and use it to make a rate table
Understand and solve proportions that use a basic ratio
Use the greatest common factor to find a basic ratio
Math Writing Prompts
End of Unit
Assessment – Form
A assessment
Performance Task if
created.
Use the greatest common factor to find a basic ratio
Differentiate proportion from non-proportion problems
Solve problems that use a basic ratio
Use greatest common factor to solve proportion problems with
greater numbers
Solve, explain and edit proportion problems
Apply mathematical concepts and skills in meaningful contexts
Reinforce the common core mathematical content standards and
mathematical practices with a variety of problem-solving situations
Math Unit 2 Overview
MATH
Grade 6
Unit 2 : Area of Polygons
Time Frame: 13 days
Key Vocabulary: perimeter, area, square unit,
base, height, square inch, square foot, square
centimeter, right angle, perpendicular, height,
base, related rectangle, right angle, height,
parallelogram, rhombus, base, perpendicular,
related rectangle, related parallelogram, acute
triangle, obtuse triangle, parallelogram, area
base, height, vertex, dimensions, trapezoid,
complex figures, pentagon, hexagon, octagon,
polygon, regular polygon, ordered pairs, regular
polygon, coordinates, tessellations
Essential Questions:
What are different strategies for finding the area of regular and irregular shapes?
What are the different strategies for finding volume of rectangular prisms?
Why is it important to know more than one strategy to find area?
Big Ideas:
Units of Area
Area of any Right Triangle
Area of any Parallelogram
Area of any Triangle
Select the Needed Measurements
Area of any Trapezoid
Area of a Complex Figure
Area of any Regular Polygon
Graph Polygons in the Coordinate Plane
Focus on Mathematical Practices
Suggested Mentor Texts:
N/A
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
6.G.1 Find the area of right triangles, other triangles, special quadrilaterals, and polygons by composing into rectangles or decomposing into triangles and other shapes; apply these techniques in the context of solving real-world and mathematical problems.
6.G.3 Draw polygons in the coordinate plane given coordinates for the vertices; use coordinates to find the length of a side joining points with the same first coordinate or the same second coordinate. Apply these techniques in the context of solving real-world and mathematical problems.
6.EE.2 Write, read, and evaluate expressions in which letters stand for numbers.
6.EE.3 Apply the properties of operations to generate equivalent expressions.
6.EE.6 Use variables to represent numbers and write
Use formulas to solve problems involving perimeter and area
Express measurements using exponents
Derive formulas for the area of a right triangle
Use formulas to solve problems involving perimeter and area
Derive formulas for the area of a parallelogram using a rectangle
Use formulas to solve problems involving perimeter and area
Find the area of any triangle
Identify the height of any triangle
Recognize that the area of a triangle is always one-half the area of
a parallelogram with the same height and base
Use formulas to solve problems involving perimeter and area
Select or infer the dimensions needed to find the area and
expressions when solving a real-world or mathematical problem; understand that a variable can represent an unknown number, or, depending on the purpose at hand, any number in a specified set.
Mathematical Practices
CC.K-12.MP.1 Make sense of problems and
persevere in solving them
CC.K-12.MP.2 Reason abstractly and
quantitatively
CC.K-12.MP.3 Construct viable arguments and
critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
CC.K-12.MP.5 Use appropriate tools
CC.K-12.MP.6 Attend to precision
CC.K-12.MP.7 Look for and make use of
structure
CC.K-12.MP.8 Look for and express regularity in
repeated reasoning
Solve real-world problems
Derive the formula for the area of a trapezoid
Use formulas to solve problems involving perimeter and area
Decompose complex figures into simpler figures
Solve problems involving perimeter and area
Decompose regular polygons into triangles
Solve problems involving perimeter and area
Draw polygons in the coordinate plane
Use coordinates to determine the side lengths of polygons
Solve real world problems
Apply mathematical concepts and skills in meaningful contexts
Reinforce the common core standards and mathematical practices
with a variety of problem-solving situations
(Quick Quiz 2)
Math Writing Prompts
End of Unit
Assessment – Form
A assessment
Performance Task if
created.
Math Unit 3 Overview
MATH
Grade 6
Unit 3 : Operations with Whole Number,
Fractions and Decimals
Time Frame: 23 days
Key Vocabulary: dividend, divisor, quotient,
remainder, ungrouping, numerator, denominator,
equivalent fractions, simplifying, unsimplifying,
common factor, common denominator, least
common multiple, reciprocal
Essential Questions:
How do operations illustrate the relationships between numbers?
How do we solve real world problems involving fractions and decimals?
How does knowing the relationship between divisors and quotients help me be a better
mathematician?
Big Ideas:
Multiplication and Division of Whole Numbers and Decimals
Relating, Composing, and Decomposing Decimals and Fractions
Multiplying Fractions and Dividing with Fractions and Whole Numbers
Dividing a Fraction by a Fraction
Suggested Mentor Texts:
N/A
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
6.NS.1 Interpret and compute quotients of fractions, and solve word problems involving division of fractions by fractions, e.g., by using visual fraction models and equations to represent the problem.
6.NS.2 Fluently divide multi-digit numbers using the standard algorithm.
6.NS.3 Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.
6.NS.4 Find the greatest common factor of two whole numbers less than or equal to 100 and the least common multiple of two whole numbers less than or equal to 12. Use the distributive property to express a sum of two whole numbers 1-100 with a common factor as a multiple of a sum of two whole numbers with no common factor.
Mathematical Practices
CC.K-12.MP.1 Make sense of problems and
persevere in solving them
CC.K-12.MP.2 Reason abstractly and
quantitatively
CC.K-12.MP.3 Construct viable arguments and
critique the reasoning of others
CC.K-12.MP.4 Model with mathematics
Review meanings of place value
Review multidigit division with whole numbers
Use appropriate strategies to estimate and adjust multipliers in
division problems
Review subtraction and regrouping strategies
Observe patterns in multiplication by 0.1 and 0.01
Multiply by a decimal
Observe patterns in division by 0.1 and 0.01
Divide by a decimal divisor
Identify whether a situation requires multiplication or division
Understand how the size of the multiplier affects the size of the
product
Place the decimal points in products and quotients
Compare fractions and decimals
Add and subtract fractions, mixed numbers and decimals
Write equivalent fractions and decimals
Add, subtract, and compare fractions and decimals with different
unit fractions or different numbers of decimal places
Find common denominators when the denominators have not
common factors and are not multiples
Discuss different strategies for finding a common denominator
Write equations to solve real world problems involving fractions
Why is it useful to know different forms of representing relationships between quantities?
Big Ideas:
Ratios, Fractions, Unit Rates, and Cross-Multiplying
Ratios with Tape Diagrams and Equations
Percent
Relate Different Measurement Units
Suggested Mentor Texts:
N/A
Technology:
Destination Math
Mega Math
Soar to Success
Interactive iTools
Common Core State Standards Teaching Points/Lesson Activity Description Assessment
Mathematical Content
Use tables of equivalent ratios to compare ratios
Initial Assessment –
Form A pre-test
6.RP.1 Understand the concept of a ratio and use ratio language to describe a ratio relationship between two quantities.
6.RP.2 Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship.
6.RP.3 Use ratio and rate reasoning to solve real-world and mathematical problems, e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number line diagrams, or equations.
6.EE.6 Use variables to represent numbers and
write expressions when solving a real-world or
mathematical problem; understand that a variable
can represent an unknown number, or,
depending on the purpose at hand, any number
in a specified set.
6.EE.7 Solve real-world and mathematical
problems by writing and solving equations of the
form x + p = q and px = q for cases in which p, q
and x are all nonnegative rational numbers.
6.EE.9 Use variables to represent two quantities
in a real-world problem that change in
relationship to one another; write an equation to
express one quantity, thought of as the
dependent variable, in terms of the other
quantity, thought of as the independent variable.
Analyze the relationship between the dependent
and independent variables using graphs and
tables, and relate these to the equation. For
example, in a problem involving motion at
constant speed, list and graph ordered pairs of
distances and times, and write the equation d =
65t to represent the relationship between
Graph ratios and use graphs to compare ratios
Use unit rates to describe ratios and to compare ratios
Use the unit rate strategy to solve proportion problems
Make horizontal ratio tables
Write ratios in fraction notation
Compare and contrast fractions and ratios
Use the cross-multiplication method for solving a proportion
Understand why the cross-multiplication method works
Use tape diagrams to solve proportions
Compare solving proportions with tape diagrams to other methods
Solve problems involving part-to-part ratios and part-to-whole
ratios
Describe ratios using multiplicative comparisons
Describe ratios using equations
Use and discuss a variety of methods that can be used to solve
proportion problems
Recognize problems that are not proportion problems
Understand the meaning of percent
Find equivalent fractions, decimals, and percents
Learn methods for calculating a percent of a number