The students will use ACC basketball statistics to practice the process of converting fractions to decimals then to percents and will learn how to create and edit a spreadsheet. They will then use this spreadsheet to analyze their data. This unit is done during the basketball season which takes approximately 15 weeks from the middle of November to the middle of March. Teachers must have Clarisworks to open the sample spreadsheet in the lesson, but may recreate it in another spreadsheet program.

The purpose of the task is to get students to reflect on the definition of decimals as fractions (or sums of fractions), at a time when they are seeing them primarily as an extension of the base-ten number system and may have lost contact with the basic fraction meaning. Students also have their understanding of equivalent fractions and factors reinforced.

This lesson unit is intended to help teachers assess how well students are able to interpret percent increase and decrease, and in particular, to identify and help students who have the following difficulties: translating between percents, decimals, and fractions; representing percent increase and decrease as multiplication; and recognizing the relationship between increases and decreases.

Four full-year digital course, built from the ground up and fully-aligned to the Common Core State Standards, for 7th grade Mathematics. Created using research-based approaches to teaching and learning, the Open Access Common Core Course for Mathematics is designed with student-centered learning in mind, including activities for students to develop valuable 21st century skills and academic mindset.

Working With Rational Numbers

Type of Unit: Concept

Prior Knowledge

Students should be able to:

Compare and order positive and negative numbers and place them on a number line.
Understand the concepts of opposites absolute value.

Lesson Flow

The unit begins with students using a balloon model to informally explore adding and subtracting integers. With the model, adding or removing heat represents adding or subtracting positive integers, and adding or removing weight represents adding or subtracting negative integers.

Students then move from the balloon model to a number line model for adding and subtracting integers, eventually extending the addition and subtraction rules from integers to all rational numbers. Number lines and multiplication patterns are used to find products of rational numbers. The relationship between multiplication and division is used to understand how to divide rational numbers. Properties of addition are briefly reviewed, then used to prove rules for addition, subtraction, multiplication, and division.

This unit includes problems with real-world contexts, formative assessment lessons, and Gallery problems.

Students review the properties of addition and write an example for each. Then they apply the properties to simplify numerical expressions.Key ConceptsThe properties of addition:Commutative property of addition: Changing the order of addends does not change the sum. For any numbers a and b, a + b = b + a.Associative property of addition: Changing the grouping of addends does not change the sum. For any numbers a, b, and c, (a + b) + c = a + (b + c).Additive identity property of 0: The sum of 0 and any number is that number. For any number a, a + 0 = 0 + a = a.Existence of additive inverses: The sum of any number and its additive inverse (opposite) is 0. For any number a, a + (−a) = (−a) + a = 0.These properties allow us to manipulate expressions to make them easier to work with. For example, the associative property of addition tells us that we can regroup the expression (311+49)+59 as 311+(49 +59), making it much easier to simplify.Students must be careful to apply the commutative and associative properties only to addition expressions. For example, we cannot switch the −7 and 8 in the expression −7 − 8 to get 8 − (−7). However, if we rewrite −7 − 8 as the addition expression −7 + (−8), we can swap the addends to get −8 + (−7).Goals and Learning ObjectivesUnderstand the properties of addition.Apply the properties of addition to simplify numerical expressions.

Students critique and improve their work on the Self Check. They then extend their knowledge with additional problems.Students solve problems that require them to apply their knowledge of multiplying and dividing positive and negative numbers. Students will then take a quiz.Key ConceptsTo solve the problems in the Self Check, students must apply their knowledge of multiplication and division of positive and negative numbers learned throughout the unit.Goals and Learning ObjectivesUse knowledge of multiplication and division of positive and negative numbers to solve problems.

Lesson OverviewStudents learn the definition of rational number, and they write rational numbers as ratios of integers and as repeating or terminating decimals.Key ConceptsStudents have been working with rational numbers throughout this unit, but the term rational number is formally defined in this lesson. A rational number is a number that can be written in the form pq, where p and q are integers. All the integers, fractions, decimals, and percents students have worked with so far in their math classes are rational numbers. Following are some rational numbers written as ratios of integers:36=361−1.2=−12105%=5100 −12=−12Any rational number can also be written as a decimal that terminates or that repeats forever in a regular pattern. For example, 35 = 0.6 and 711 = 0.63636363… Repeating decimals are often written with a bar over the digits that repeat. For example, 0.63636363… can be written as 0.63¯.There are numbers that are irrational. These numbers include π and the square root of any whole number that is not a perfect square, such as 2. The decimal form of an irrational number does not terminate, and the digits do not follow a repeating pattern. Students will study irrational numbers in Grade 8.Goals and Learning ObjectivesUnderstand the definition of rational number.Write rational numbers as ratios of integers.Write rational numbers as terminating or repeating decimals.SWD: Students with disabilities may have difficulty working with decimals and fractions, especially moving between the two. If students demonstrate difficulty to the point of frustration, provide direct instruction on the basics for finding equivalent fractions and decimals.ELL: Target and model key language and vocabulary. Specifically, focus on the term rational, as well as terms such as terminate. As you’re discussing the key points, write the words on the board or on large sheets of paper and explain/demonstrate what the words mean. Since these are important points that students will be using throughout the module, write them on large poster board so that students can use them as a reference. Have students record new terms, definitions, and examples in their Notebook. 

The purpose of the task is to have students reflect on the meaning of repeating decimal representation through approximation. A formal explanation requires the idea of a limit to be made precise, but 7th graders can start to wrestle with the ideas and get a sense of what we mean by an "infinite decimal."

This lesson unit is intended to help teachers assess how well students are able to understand and use directed numbers in context. It is intended to help identify and aid students who have difficulties in ordering, comparing, adding, and subtracting positive and negative integers. Particular attention is paid to the use of negative numbers on number lines to explore the structures: starting temperature + change in temperature = final temperature final temperature Đ change in temperature = starting temperature final temperature Đ starting temperature = change in temperature.