Units
Unit 1: Equivalent Representations and Uses of Numbers
Big Ideas:
There are many equivalent representations for a number or numerical relationship. Each representation may emphasize something different about that number or relationship.
Learning Targets:
Students will know...
there is more than one way to show a number or relationship.
equivalent values of benchmark fractions, decimals and percents
Students will be able to...
find equivalent values of rational numbers in multiple forms (fractions, decimals and percents).
determine reasonableness of an equivalent value using models.
gain a sense of the size of numbers by comparing them to familiar benchmark numbers.
represent part to whole comparisons in fraction, decimal, and percent formats.
Essential Questions:
How do situations influence the best numerical representations?
What are the benefits of mathematical models?
Unit 2: Locate and Order Rational Numbers
BIg Ideas:
Applying math to different real-world situations requires various numerical representations. Values of numbers determine their order and location.
Learning Targets:
Students will know...
that numbers can be grouped by their attributes.
rational number relationships displayed by a Venn diagram or other visual representation (include whole numbers, integers, rational numbers).
that all numbers have an opposite.
absolute value is the positive distance from zero.
division may be represented as fractions.
Students will be able to...
determine to which group(s) a number belongs.
determine the order of numbers (all types of rational numbers) using a number line.
find any number's absolute value.
use ordered pairs to locate points in any of the four quadrants.
Essential Questions:
How does comparing quantities describe the relationship between them?
Why would we want to classify numbers?
How do we use numerical relationships to compare numbers?
Unit 3: Operations and Applications of Integers and Positive Rational Numbers
Big Ideas:
There are some mathematical relationships that are always true and these relationships are used as the rules of arithmetic and algebra and are useful for writing equivalent forms of expressions and solving equations and inequalities.
Learning Targets:
Students will know...
multiplying by a rational number less than 1 causes a decrease.
multiplying by a rational number greater than 1 causes an increase.
the relationship between addition and subtraction of rational numbers
the relationship between division and multiplication of rational numbers
Students will be able to...
combine and separate parts of numbers.
solve rational number operations with concrete, pictorial, and algebraic models.
Essential Questions:
How can mathematical operations with rational numbers help us make real life decisions?
How does understanding numerical operations provide a basis for understanding more complex mathematical operations?
How does the ability to use multiple methods and tools help simplify mathematical tasks involving fractions and decimals?
Unit 4: Understand and Apply Ratios, Rates and Percents
Big Ideas:
Proportional relationships express how quantities change in relationship
to each other. Predictions and comparisons can be made based on the understanding of proportional relationships.
Learning Targets:
Students will know...
ratios are part to part and part to whole comparisons of two different quantities.
similarities and differences between ratios and rates.
similarities and differences between additive and multiplicative relationships.
differences between qualitative and quantitative reasoning
Students will be able to...
write mathematical proportions that correspond to given situations.
create graphs, tables, and proportions given a ratio or rate.
create concrete and pictorial models of proportional relationships.
solve real-world problems using equivalent ratios, including percent problems.
use proportions to convert measurements within the same system.
give a solution based on qualitative reasoning.
give a solution based on quantitative reasoning.
verify if two quantities are proportional.
Essential Questions:
When is it appropriate to reason proportionally?
How do proportions relate to percents?
Why is it important to determine proportionality?
Unit 5: Generate Equivalent Mathematical Expressions
Big Ideas:
Numerical expressions can represent mathematical situations and structures in many equivalent forms using mathematical properties. The understanding of order of operations and mathematical properties promote computational fluency.
Learning Targets:
Students will know...
there is an order to operations so that everyone gets the same value when evaluating a numerical statement.
various properties used to manipulate expressions.
Students will be able to...
use mathematical symbols to model verbal expressions.
evaluate expressions and use expressions to solve problems.
find the prime factorization of a number.
simplify expressions using properties and order of operations.
Essential Questions:
How can algebraic symbols be used to efficiently express mathematical situations?
How is thinking algebraically different from thinking arithmetically?
How do the properties contribute to algebraic understanding?
Unit 6: Represent Multiplicative and Additive Relationships
Big Ideas:
Patterns and relationships can be represented in various ways. Within these patterns and relationships one quantity is independent and the other is dependent.
Learning Targets:
Students will know...
the difference between independent and dependent quantities.
similarities and differences between additive and multiplicative relationships.
Students will be able to...
determine the independent quantity of a situation.
determine the dependent quantity of a situation.
create multiple representations (verbal description, equations, tables and graphs) of a situation.
Essential Questions:
How can patterns of change be represented in multiple ways?
How are variables in the real-world related to each other?
Unit 7: Represent, Solve and Graph One-Step Equations and Inequalities
Big Ideas:
Real-world situations can be represented symbolically. Algebraic expression, equations, and inequalities generalize relationships from specific cases.
Learning Targets:
Students will know...
mathematical properties (inverse, identity, associative, commutative, distributive).
solutions can be represented on a number line.
a situation can be represented by a verbal description or algebraically.
Students will be able to...
write an equation or inequality given a situation.
write a situation given an equation or inequality.
use mathematical properties to transform algebraic equations and inequalities.
substitute values into equations or inequalities to determine equivalence.
use previous geometric knowledge to solve equations and inequalities.
use a number line to graph solutions.
Essential Questions:
How is thinking algebraically different from thinking arithmetically?
How do I use algebraic expressions to analyze or solve problems?
How do the properties contribute to algebraic understanding?
What is meant by equality?
Unit 8: Convert Measurements Within the Customary System
Big Ideas:
Different characteristics are measured using different units of measure. There are two systems that are used to measure length, weight, and capacity. These systems are the customary and metric systems of measurement.
Learning Targets:
Students will know...
the difference between the metric and customary measurement systems.
the basic units of each system.
the meaning of the suffixes of the metric system.
Students will be able to...
use proportions to convert measurements within the same system.
use reference materials to solve conversion problems.
Essential Questions:
When are exact measures needed?
How might converting within a measurement system be helpful?
Unit 9: Apply Understanding of Sides and Angles of Triangles
Big Ideas:
All triangles share certain relationships between their sides and angles. Understanding these relationships can assist in finding missing measurements.
Learning Targets:
Students will know...
interior angle measurements for triangles.
the relationship between the three sides of a triangle.
Students will be able to...
use relationships of triangles to solve for missing measurements.
Essential Questions:
When are exact measures needed?
How do you determine the critical measures needed to determine the shape of a polygon?
What is the relationship between sides and angles of shapes?
Unit 10: Model, Connect and Solve Geometric Equations for Area and Volume
Big Ideas:
Students explore shapes by decomposing and rearranging to find relationships between different shapes. The purpose for which a measurement is calculated will determine what formula and unit will be used in calculating the measurement. Geometric relationships exist between 2-dimensional and 3-dimensional figures.
Learning Targets:
Students will know...
all 2-d figures have area.
all 3-d figures have area and volume.
attributes of various figures (rectangles, parallelograms, trapezoids, triangles, and rectangular prisms).
the representation of variables of various formulas.
interior angle measurements for triangles.
polygons can be decomposed into simpler shapes.
what types of units are necessary for finding the area of two-dimensional figures and three-dimensional figures.
Students will be able to...
connect concrete and pictorial models to formulas for area and volume.
use reference materials to solve area and volume problems.
rearrange parts of a shape to find its area.
Essential Questions:
When are exact measures needed?
How do you determine the critical measures needed to find the area or volume of a given shape?
What is the relationship between shapes having the same base and height measure?
Unit 11: Data Representation and Analysis
Big Ideas:
Data can be modeled and analyzed in various ways. The type of data determines the graphical representation that can be used. All sets of data have a center, shape and spread.
Learning Targets:
Students will know...
various ways to display data.
different data displays have different purposes.
if a set data does or does not yield variability.
the purposes of mean, median, mode, range, and interquartile range.
Students will be able to...
determine mean, median, mode, range, and interquartile range of a set of data from different representations.
use measures of central tendencies to describe the distribution of a set of data.
collect data
create and interpret a variety of graphical representations.
Essential Questions:
How does the type of data influence the choice of display?
How can data be compared?
How can data analysis help to interpret and make predictions about real life situations?
Unit 12: Personal Financial Literacy
Big Ideas:
Basic financial literacy is critical in all people's lives. Financial planning and responsibility are enduring habits of individual fiscal responsibility. Individual choices directly influence occupational goals and future earnings potential.
Learning Targets:
Students will know...
the difference between cash, checks, debit cards, and credit cards.
the difference between good and bad debt.
how career choice, education, entrepreneurship, and economic conditions effect income.
appropriate services provided by financial institutions.
institutes of higher education is possible through various avenues of funding.
Students will be able to...
establish a positive credit history.
determine consumer power according to occupation.
research methods of paying for institutes of higher learning.
keep balanced checking and savings accounts.
Essential Questions:
What can I do to ensure that I will be successful when making and managing money?
How will developing effective spending habits affect my financial future?
Unit 13: STARR Preparation
Review of all Units