Unit 1: Operations with Rational Numbers
Students develop a unified understanding of numbers, recognizing
fractions, decimals (that have a finite or a repeating decimal representation),
and percents as different representations of rational numbers.
Students extend addition, subtraction, multiplication, and division to all
rational numbers, maintaining the properties of operations and the relationships
between addition and subtraction, and multiplication and division. By applying
these properties, and by viewing negative numbers in terms of everyday
contexts (e.g., amounts owed or temperatures below zero), students explain and
interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one variable and use these equations to solve problems.
2A - Expressions
Students build on their understanding of order of operations
and use the properties of operations to rewrite equivalent numerical expressions that were developed in Grade 6. Students continue to use properties that were initially used with whole numbers and now develop the understanding that properties hold for integers, rational and real numbers.
Opportunities build upon this experience of writing expressions using
variables to represent situations and use the properties of operations to
generate equivalent expressions. Moreover, students should use substitution to understand that expressions are equivalent. By substituting a numerical value for the variable and evaluating the expression, students can see that expressions written in different ways can also be equivalent to one another. Students should use and understand the properties of operations. These include: the commutative, associative, identity, and inverse properties of addition and of multiplication, and the zero property of multiplication. This is a continuation of work from 6th grade using properties of operations and combining like terms.
2B - Equations
Furthermore, students will understand the connections between performing
the inverse operation and undoing the operations are used appropriate. Students
are expected to show their steps in their work and explain their thinking using
the correct terminology for the properties and operations.
Students’ understanding and application of writing and solving one-step
equations from a problem situation to multi-step problem situations is built.
This is also the context for students to practice using rational numbers
including: integers, and positive and negative fractions and decimals. As
students analyze a situation, they identify what operation should be completed
first, then the values for that computation. Each set of the needed operation
and values is determined in order. Finally an equation matching the order of
operations is written. Multiple opportunities for students to work with multi-step problem situations that have multiple solutions and therefore can be represented by an inequality are provided. Students become aware that values can satisfy an inequality but not be appropriate for the situation, therefore limiting the solutions for that particular problem.
Unit 3: Ratios & Proportional Relationships
Students extend their understanding of ratios and develop understanding of proportionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar objects. Students graph proportional relationships and understand the unit rate
informally as a measure of the steepness of the related line, called the slope.
They distinguish proportional relationships from other relationships.
Unit 4: Geometry
Students continue their work with area from Grade 6, solving
problems involving the area and circumference of a circle and surface area of
three-dimensional objects. Students will reason about relationships among
two-dimensional figures using informal geometric constructions, and they gain
familiarity with the relationships between angles formed by intersecting lines.
Students work with three-dimensional figures, relating them to two-dimensional
figures by examining cross-sections. They solve real-world and mathematical
problems involving area, surface area, and volume of two- and three-dimensional
objects composed of triangles, quadrilaterals, polygons, cubes and right prisms.
Unit 5: Inferences
Students build on their previous work with single data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the importance of representative samples for drawing inferences.
Unit 6: Probability
In Grade 7, students will concentrate on understanding that
good answers to statistical questions depend upon a good plan for collecting
data relevant to the questions of interest. Because statistically sound data
production is based on random sampling, a probabilistic concept, students must
develop some knowledge of probability before launching into sampling. Their
introduction to probability is based on seeing probabilities of chance events as
long-run relative frequencies of their occurrence, and many opportunities to
develop the connection between theoretical probability models and
empirical/experimental probability approximations. This connection forms the
basis of statistical inference.