Khan Aacdemy provides free resources for teachers and students in various subjects. In the subject of Math, you can videos; tutorials, and practice for your students.
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- Material Type:
- PBS LearningMedia
- Provider Set:
- PBS Learning Media: Multimedia Resources for the Classroom and Professional Development
- U.S. Department of Education
- Date Added:
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.
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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
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.
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.
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.