SAU #35 Grade 7 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 #1: Develop number sense, ways to represent numbers, and an understanding of the relationships among numbers and our numeration system.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
1.1.1 Know and use divisibility rules for 2, 3, 4, 5,6, 9, and 10.

1.1.2 Given a whole number list all of its factors.

1.1.3 Rewrite any whole number into its prime factorization.

1.1.4 Use divisibility rules, factors, multiples, prime factorization, and relatively prime numbers to solve problems.

1.1.5 Given a whole number list multiples of that number.

1.1.6 Explore squares and square roots using visual models.

1.1.7 Use visual models to compare and order fractions and mixed numbers.

1.1.8 Develop and apply the meaning of a fraction in terms of a ratio.

1.1.9 Represent division as a fraction (numerator divided by denominator).
 

1.1.10 Use graphic organizers to depict relationships among sets of numbers.

1.1.11 Demonstrate the relationship of decimals to fractions and vice versa.

1.1.12 Explore the connections among decimals, fractions, and percents.

1.1.13 Recognize equivalent ratios.

1.1.14 Use exponents to demonstrate repeated multiplication.

  
 


 


 



 

Area = 5
Edge Length = √5


 


 


 

Divide 3 pizzas between 8 people: 3÷8 = 3/8 pizza per person

Natural numbers, whole numbers, integers, positive rationals.

 


 

Write three ratios equivalent to 6:8
 

Factor Game, Product Game

Numbers, Numeration, Operations, and Number Theory

Broad Goal #2: Students will understand the meanings of and relationships between number operations and their properties.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
1.2.1 Introduce the concept of absolute value when working with integers.

1.2.2 Develop operation sense with rational numbers.





.2.3 Use and identify the distributive, associative, and commutative properties and the identity properties for addition and multiplication with rational numbers.

  
 

Multiplying by a fraction less than one results in a smaller number and vice versa.
 

Use open-ended questions:
* find a fraction and a decimal whose product is between 1 and 2.
* find 2 numbers between 0 and 1 whose quotient is between 8 and 10.

Numbers, Numeration, Operations, and Number Theory

Broad Goal #3: Compute accurately and efficiently and make reasonable estimates.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
1.3.1 Add and subtract fractions with unlike denominators.

1.3.2 Use visual models to develop the concept of multiplication of fractions.

1.3.3 Develop the concept of division of fractions through visual models, algorithms, the relationship to multiplication.



 



1.3.4 Develop and apply algorithms to perform the four basic operations with integers.

1.3.5 Develop and use different strategies to estimate the results of computations with whole numbers, integers, and fractions and judge the reasonableness of the results.

1.3.6 Apply order of operations when simplifying expressions to include symbols of inclusion and powers and roots.

1.3.7 Develop fluency in operations on rational numbers.

  
 


 

Divide numerators and divide denominators:
4/6 ÷ 1/2 = 4/3

Use a common denominator and divide numerators:
4/6 ÷ 3/6 = 4/3

Multiply by the inverse: 2/3 x 2/1 = 4/3.

  

Geometry and Measurement

Broad Goal #1: Explore and analyze the properties and relationships of two- and three-dimensional shapes and figures.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
2.1.1 Build a working vocabulary relating to shapes and their characteristics.
 



 



 



 





 

2.1.2 Create geometric figures, given definitions and/or properties, using a variety of tools.


2.1.3 Describe the types of angles in a polygon (interior, central, exterior) and determine the measure of each type for any given regular polygon.

2.1.4 Plot points on a coordinate graph understanding the nature of positive and negative axes.

   Polygon vocabulary, motion vocabulary, classifications.

Polygon examples: quadrilateral, triangles, hexagons and the like

Motion vocabulary examples: Symmetry, rotation, reflection

Classification  examples:Scalene, regular, isosceles

Relationship examples: Congruent, parallel, perpendicular, adjacent and opposite sides of a right triangle

 

 

 

 

 

 

 

 Isosceles Triangle Search,Blind Triangle Check,Wheel Project (Resource - Marie Snyder).

Flags of the World

Get it Together – Equals project at Berkley Hall of Science


 







 

Straight-edge, compass, geoboard, mirror, protractor, pattern blocks, MIRA

Geometry and Measurement

Broad Goal #2: Develop spatial reasoning and visualization techniques and skills.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
2.2.1 Sketch specific two-dimensional figures, given definitions and/or properties.

2.2.2 Draw and construct two and three-dimensional objects using various tools.

2.2.3 Use manipulatives and technology to model situations geometrically and to solve problems in mathematics and other curricular areas.

  


Technology, straightedge, and compass.
 

 

Geometry and Measurement

Broad Goal #3: Students will use geometric transformations to analyze situations and solve problems.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
2.3.1 Understand the effects of reflections, translations, and rotations in the study of congruence.

2.3.2 Understand the effects of dilations in the study of similarity.

 

 

 		    Wheel Project (Resource - Marie Snyder)
Flags of the World

 

Geometry and Measurement

Broad Goal #4: Students will understand and apply the units, systems, and process of measurement: one-, two-, and three-dimensional measurement.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
2.4.1 Draw and measure angles with a protractor.

2.4.2 Use formulas, approximations, or computer geometry programs to determine perimeters, areas and volumes.

2.4.3 Choose the appropriate unit of measurement (units, square units, and cubic units) to determine the perimeter of polygons, circumference of circles, area of polygons and circles, the volume and surface area of prisms and cylinders.

2.4.4 Choose appropriate units of linear measure and convert between units.




2.4.5 Understand and apply the relationship between like units of square measure and like units of cubic measure.


2.4.6 Understand and describe the relationships between perimeter and area of various polygons.


 

2.4.7 Use ratio and proportions to explore the properties of similar figures and use these properties to solve problems.

  
 



 






 

How many feet in 2.5 miles within the English system and how many meters in 2.5 kilometers within metric system.

9 square feet = 1 square yard; 1000 cubic millimeters = 1 cubic centimeter.

Can two figures have the same area and different perimeters? If the perimeter of a rectangle is doubled, what happens to the area?

  

Geometry and Measurement

Broad Goal #5: Students will understand and apply the units, systems, and processes of measurement: other types of measurement.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
2.5.1 Be able to identify and label parts of a right triangle in relation to a given angle.

 

 		     

Data Analysis, Statistics, and Probability

Broad Goal #1: Students will use data analysis, statistics, and probability to analyze and model situations and the outcomes of experiments.

7th 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 Demonstrate an understanding of mean, median, and mode and calculate these measures of central tendency.

3.1.3 Understand the meaning of and differences between measurement data and categorical data.

3.1.4 Distinguish between theoretical and experimental probability.

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

3.1.6 Compute and interpret the probability of outcomes using simple probability experiments and real world situations.

3.1.7 Compute the probability of simple compound events using organized lists, tree diagrams, and area models.

3.1.8 Design and use sampling techniques.



3.1.9 Given a set of data, choose an appropriate display.

  
 



 

Differences between quantitative and qualitative


 

Fraction, simplest form, decimal, percentage

Weather, lotteries, medical testing
 



 

Random sample, systematic sampling, convenience sampling.

  

Functions, Relations, and Algebra

Broad Goal #1: Students will recognize and describe patterns.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
4.1.1 Recognize, describe, analyze, extend, generalize, and create a variety of patterns using models, tables, graphs, and simple rules

4.1.2 Describe and extend numeric and geometric patterns.

      

Functions, Relations, and Algebra

Broad Goal #2: Students will represent, analyze, and model mathematical situations and structures.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
4.2.1 Understand and use the notion of variable as a varying quantity.

4.2.2 Use substitution to evaluate expressions.

4.2.3 Solve one-step questions.

      

Functions, Relations, and Algebra

Broad Goal #3: Students will analyze change in various contexts.

7th Grade
Student Outcomes Alignment Examples Resources/Activities
4.3.1 Describe how a change in one quantity results in another.


4.3.2 Use proportional reasoning strategies to solve problems.

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

Equivalent fractions, cross products and looking at factors.