This lesson unit is intended to help teachers assess how well students …

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 …

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 …

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 use the Hot Air Balloon interactive to model integer addition. They …

Students use the Hot Air Balloon interactive to model integer addition. They then move to modeling addition on horizontal number lines. They look for patterns in their work and their answers to understand general addition methods.Key ConceptsTo add two numbers on a number line, start at 0. Move to the first addend. Then, move in the positive direction (up or right) to add a positive integer or in the negative direction (down or left) to add a negative integer.Here is −6 + 4 on a number line: The rule for integer addition (which extends to addition of rational numbers) is easiest to state if it is broken into two cases:If both addends have the same sign, add their absolute values and give the result the same sign as the addends. For example, to find −5 + (−9), first find |−5| +|−9| = 14. Because both addends are negative the result is negative. So, −5 + (−9) = −14.If the addends have different signs, subtract the lesser absolute value from the greater absolute value. Give the answer the same sign as the addend with the greater absolute value. For example, to find 5 + (−9), find |−9| − |5| = 9 − 5 = 4. Because −9 has the greater absolute value, the result is negative. So, 5 + (−9) = −4.Goals and Learning ObjectivesModel integer addition on a number line.Learn general methods for adding integers.

Students use the Hot Air Balloon simulation to model integer subtraction. They …

Students use the Hot Air Balloon simulation to model integer subtraction. They then move to modeling subtraction on a number line. They use patterns in their work and their answers to write a rule for subtracting integers.Key ConceptsThis lesson introduces the number line model for subtracting integers. To subtract on a number line, start at 0. Move to the location of the first number (the minuend). Then, move in the negative direction (down or left) to subtract a positive integer or in the positive direction (up or right) to subtract a negative integer. In other words, to subtract a number, move in the opposite direction than you would if you were adding it.The Hot Air Balloon simulation can help students see why subtracting a number is the same as adding the opposite:Subtracting a positive number means removing heat from air, which causes the balloon to go down, in the negative direction.Subtracting a negative number means removing weight, which causes the balloon to go up, in the positive direction.The rule for integer subtraction (which extends to addition of rational numbers) is easiest to state in terms of addition: to subtract a number, add its opposite. For example, 5 – 2 = 5 + (–2) = 3 and 5 – (–2) = 5 + 2 = 7.Goals and Learning ObjectivesModel integer subtraction on a number line.Write a rule for subtracting integers.

This lesson unit is intended to help teachers assess how well students …

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.

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