SAU #35 Grade 6 Mathematics
Strand: Numbers, Numeration, Operations, and Number Theory
Broad Goals
Develop number sense, ways to represent numbers, and an understanding of the relationships among numbers and our numeration system. Students will understand the meanings of and relationships between number operations and their properties. Compute accurately and efficiently and make reasonable estimates.

 

Strand: Geometry and Measurement

Broad Goals

Explore and analyze the properties and relationships of two- and three-dimensional shapes and figures.

Develop spatial reasoning and visualization techniques and skills.

Students will use geometric transformations to analyze situations and solve problems.

Students will understand and apply the units, systems, and process of measurement: one-, two-, and three-dimensional measurement.

Students will understand and apply the units, systems, and processes of measurement: other types of measurement.

 

Strand: Data Analysis, Statistics, and Probability

Broad Goal

Students will use data analysis, statistics, and probability to analyze and model situations and the outcomes of experiments.

 

Strand: Functions, Relations, and Algebra
Broad Goals
Students will recognize and describe patterns. Students will represent, analyze, and model mathematical situations and structures. Students will analyze change in various contexts.

Numbers, Numeration, Operations, and Number Theory

Broad Goal: Develop number sense, ways to represent numbers, and an understanding of the relationships among numbers and our numeration system.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
1.1.1 Read and write integers and positive rational numbers.

1.1.2 Relate the base 10 value system to the metric system.

1.1.3 Demonstrate the meaning of 10%, 25%, 50%, 75%, and 100%, and their fractional and decimal equivalents.

1.1.4 Express simple ratios as percents and percents as ratios with a denominator of 100.

1.1.5 Given an integer or positive rational number, represent the number using diagrams, or physical models.

1.1.6 Model, name and write equivalent fractions.

1.1.7 Demonstrate the relationship of simple decimals to fractions and vice versa.


1.1.8 Given a pair of fractions, determine which is greater by using physical models, illustrations, or by reasoning.

1.1.9 Develop and use order relationships for positive and rational numbers.

1.1.10 Explore order relations for integers.

1.1.11 Explore ancient numeration systems and the use of different bases.

1.1.12 Identify multiples and factors of whole numbers.

1.1.13 Identify numbers that are divisible by 2, 3, 5, 6, 9, and 10.

1.1.14 Apply number theory concepts to the factoring of whole numbers and the equivalency of rational numbers.

1.1.15 Introduce the concept of division as a fraction (numerator divided by denominator).

1.1.16 Use the area model to develop the concept of square numbers.

1.1.17 Read and write whole numbers, including numbers through the trillions.

1.1.18 Represent and compare whole numbers and decimals, emphasizing place value structure of the base 10 number system.

  

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


EDM
Lesson 6.3-4

  

 

 

.25, 1/4, 25%

 

 

 


Number lines or thermometers

 



Use money or rulers to show 0.1 equals 1/10 or 1/4 equals .25).

 

 

 

 

 

 


Base 2 and 5

 

 

 


Prime numbers and greatest common factor

 Math Advantage 2000

Visual Math II – Lessons 5-8

 

Visual Math – Math Alive! Course II

 

 

 

 

 


Paper folding for fractions.
Fraction Top It – card game

 

 


Connected Math: Bits & Pieces II

 

 

 

 

 

 

 

 

 

 

 

 

www.funbrain.com/linejump/index.html

Numbers, Numeration, Operations, and Number Theory

Broad Goal: Students will understand the meanings of and relationships between number operations and their properties.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
1.2.1 Demonstrate an understanding of the four basic operations and the relationships among them.


1.2.2 Develop the concepts of addition and subtraction of fractions and decimals using manipulatives.

1.2.3 Apply the associate and commutative properties for addition and multiplication and the distributive property.

1.2.4 Apply the multiplicative and additive properties of zero, and the multiplicative property of one.

1.2.5 Explain why the product of two whole numbers greater than 1 is greater than either of the factors.

1.2.6 Demonstrate an understanding that when dividing two whole numbers that are greater than 1, the quotient will be smaller than the dividend.

   One model of multiplication is repeated addition, subtraction is the inverse of addition.

 

 

25 x (17X40) = (25X40) x 17; 7 x (19) = 7 x (20-1) and 7 x (20-1) = 7 x 20-7

47 + 19 = 47 + -7; 1 = 2/2 and 2/2 x 3/4 = 6/8, thus 3/4 = 6/8

 

 


12 divided by 4 = 3

  

Numbers, Numeration, Operations, and Number Theory

Broad Goal: Compute accurately and efficiently and make reasonable estimates.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
1.3.1 Demonstrate mastery of the multiplication facts with factors less than or equal to 10.

1.3.2 Add integers using models or representations.



1.3.3 Multiply three-digit whole numbers by 2-digit whole numbers.

1.3.4 Divide three-digit whole numbers by 2-digit whole numbers.

1.3.5 Develop and use algorithms for multiplication and division of decimals.

1.3.6 Use models to introduce algorithms for multiplication and division of decimals.

1.3.7 Using physical models and illustrations, determine the sum or difference of fractions with any like denominators.

1.3.8 Make appropriate estimations relating to quantity, capacity, volume, and elapsed time.

1.3.9 Develop, encourage, and use efficient algorithms for multiplication and division.

1.3.10 Know about and be able to use variety of mental computation techniques.

1.3.11 Select and use appropriate mental computation and estimations strategies in problem situations and to determine the reasonableness of answers.


1.3.12 Use correct order of operations in making computations, including use parentheses.

 

 		   

 

The red-black chip model, number lines, or money.

 

 

 

 

Lattice Method for Multiplication


Area model

 

 

 

 

 

 

 

 

 

 


Using compatible numbers and applying properties of operations.

 Mad Minutes

 

AIMS "Integrated Rule Practice" Activity
Maths300 Protons & Antiprotons Activity

 

 

 

 

 

 

 

 

 

 

 

 

Mental Math in the Middle Grades – Dale Seymour

Geometry and Measurement

Broad Goal: Explore and analyze the properties and relationships of two- and three-dimensional shapes and figures.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
2.1.1 Identify, describe, and name properties of common two- and three-dimensional objects (Specifically triangles and quadrilaterals; cubes, rectangular and triangular prisms).

2.1.2 Given a geometric property, make inferences as to shape or measurement.

2.1.3 Draw congruent and similar figures.

2.1.4 Recognize and create shapes that have rotation and reflection symmetry.

2.1.5 Describe and apply the relationships among angles and side lengths in congruent and similar figures.

2.1.6 Define and classify angles as right, obtuse, acute, straight, complementary, supplementary, adjacent, or reflex angles.

  

 




 



EDM Lesson 5.6


EDM Lesson 5.5

 

 

 

EDM Lesson 5.1-5.2 and 5.9-5.10

 Sum of angle measures in any triangle is 180°

 

What different polygons have opposite sides parallel?

 AIMS

 


AIMS

 

 

Symmetry & Tesselations – Jill Britton/Dale Seymour

 

 

AIMS

Geometry and Measurement

Broad Goal: Develop spatial reasoning and visualization techniques and skills.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
2.2.1 Build and draw common two- and three-dimensional objects using manipulatives and/or computer graphics.

2.2.2 Create and describe mental images of objects, patterns, and paths.

2.2.3 Describe and build common three-dimensional objects from two-dimensional representations and vice versa.

    

 

Given a flashlight and a ball, describe the shadow of the ball.

 Ruins of Montarek – Dale Seymour

 

 

Ruins of Montarek – Dale Seymour

Geometry and Measurement

Broad Goal: Students will use geometric transformations to analyze situations and solve problems.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
2.3.1 Describe and predict the results of flips, slides, and turns on two-dimensional shapes.

2.3.2 Recognize and apply dilations (enlargements and shrinking).

2.3.3 Describe and create tessellations using geometric shapes and transformations.

      

Geometry and Measurement

Broad Goal: Students will understand and apply the units, systems, and process of measurement: one-, two-, and three-dimensional measurement.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
2.4.1 Recognize, compare and apply standard and non-standard units of measurement for length, area, and volume.

2.4.2 Use a protractor to measure angles.

2.4.3 Select and apply appropriate formulas, techniques, or tools to determine the perimeter of common two-dimensional objects.

2.4.4 Select and use estimation strategies for finding areas and volumes.

2.4.5 Choose appropriate units of linear measure and convert between like units.


2.4.6 Interpret scale drawings.

2.4.7 Describe the relationships (ratios) between the perimeters and areas of similar figures.

    

 

 

 

 

 

 

Feet and miles, within the English or metric systems.

  

Geometry and Measurement

Broad Goal: Students will understand and apply the units, systems, and processes of measurement: other types of measurement.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
2.5.1 Compare standard and non-standard units of measurement for capacity and weight.

2.5.2 Measure weights, capacities, times and temperatures using appropriate units.

2.5.3 Interpret maps and timelines.

2.5.4 Identify the time indicated by passage of hour, half-hour, and quarter-hour intervals including identifying movement from A.M. to P.M.

2.5.5 Determine how much time has passed in a given interval including both A.M. and P.M.

2.5.6 Apply the concept of time zones in problem-solving situations.

    

 

 

 

 

 


How much time has passed from 9:30 A.M. to 2:15 P.M.

  

Data Analysis, Statistics, and Probability

Broad Goal: Students will use data analysis, statistics, and probability to analyze and model situations and the outcomes of experiments.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
3.1.1 Construct and interpret line plots, stem and leaf plots, and frequency distributions.

3.1.2 Use simulations to model real world situations (including simulations that involve technology.

3.1.3 Demonstrate an understanding of mean, median, and mode and calculate these measures of central tendency.

3.1.4 Design and use sampling techniques to make predictions and explain how data collection methods affect the nature of the data set.

3.1.5 Represent the likelihood of an event by a number from 0 to 1.

      

Functions, Relations, and Algebra

Broad Goal: Students will recognize and describe patterns.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
4.1.1 Recognize, describe, analyze, extend, generalize, and create a wide variety of patterns, using models, tables, graphs, and simple rules.

4.1.2 Use calculators, computers, and other technology to create patterns and analyze relationships.

 

 

 		     

Functions, Relations, and Algebra

Broad Goal: Students will represent, analyze, and model mathematical situations and structures.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
4.2.1 Represent situations, number patterns, and inequalities with standard algebraic notations.

4.2.2 Understand and use the notion of variable as an unknown quantity represented by a letter or symbol.

4.2.3 Plot points on a rectangular coordinate system.

4.2.4 Analyze simple linear equations with one variable using concrete materials, tables or graphs.

4.2.5 Use reasoning and intuition to solve simple linear equations with one variable.

      

Functions, Relations, and Algebra

Broad Goal: Students will analyze change in various contexts.

6th Grade
Student Outcomes Alignment Examples Resources/Activities
4.3.1 Describe how a change in one quantity results in a change in another within a functional relationship.

4.3.2 Quantify and interpret rates of change in discrete (i.e. cost per unit) and in continuous (i.e. distance per unit of time) settings.

   How a change in length or width affects perimeter, area, and volume.