Unit 3

Math

Unit Length and Description:

25 days

In this unit students will use prior learning to as they are adding and subtracting fractions with unlike denominators using concrete and visual models, reasoning and equations.  They develop conceptual understanding of addition and subtraction of fractions and mixed numbers in order to solve real-world problems.  Quantitative reasoning will be used by students to determine whether their answers are reasonable.

Students use visual models such as area models, fraction strips, or number lines as they begin to add fractions with unlike denominators.  Students begin to understand the need for like denominators by using concrete models.  Once students understand the need for like denominators and can identify appropriate denominators, then they begin using the algorithm. Students understand that when they are finding equivalent fractions, they are multiplying the original fraction by names for 1.

Students solve problems involving addition and subtraction of fractions with unlike denominators.  Students also use benchmarks, comparisons and mental math to justify their thinking and to determine whether their answer is reasonable.

Students extend their previous work with considering a fraction as a division situation to expressing the quotient of a division problem as a fraction or mixed number.  Real-life problems should provide the context in which expressing the fraction as a remainder makes sense.  Students are provided with a variety of division problems to model interpreting the remainder as a fraction.

Standards:

Enduring Understandings:

·        Landmark/benchmark numbers should be used when making decisions about other numbers.

·        Models can be used to compute fractions with like and unlike denominators.

·        The same fractional amount can be represented by an infinite set of equivalent fractions.

·        A fraction describes the division of a whole into equal parts, and it can be interpreted in more than one way depending on the whole to be divided.

·        Multiplying a whole number by a fraction involves division as well as multiplication.  The product is a fraction of the whole number.

·        Rounding and compatible numbers can be used to estimate the product of fractions or mixed numbers.

·        The relative size of the factors can be used to determine the relative size of the product.

Essential Questions:

·        Why would I need to use landmark/benchmark numbers when making decisions about other numbers?

·        How can models (line plots, etc.) be used to compute fractions with like and unlike denominators?

·        What strategies can be used to determine if answers are reasonable?

·        How can I tell if a fraction is greater than, less than, or equal to one whole.

·        How can fractions with different denominators be added together?  Subtracted?

·        How are fractions related to division?

·        How can I multiply fractions and whole numbers?

·        How does multiplying by a fraction change the other factor?