Unit 3: Fraction Operations
Topics 7, 8 & 9 in enVision; see Pearson app on webdesk.pisd.edu
Students will understand that…
U1 There are many ways to represent a quantity but the best way is based on the problem in front of you.
U2 Objects, pictures, and numbers can be used to represent problem situations.
U3 There are multiple strategies and methods for finding an accurate mathematical solution.
Students will know …
K1 prime numbers have only two factors - one and itself.
K2 composite numbers have more than two factors.
K3 the relationship between the different parts and wholes when adding and subtracting fractions.
K4 positive rational numbers are numbers that can be represented as fractions.
K5 fractions can be represented in more than one way.
K6 properties of operations apply to fractions.
K7 the relationship between mixed numbers and improper fractions.
K8 the word “of” indicates multiplication when used with fractions.
K9 the product of a whole number and a unit fraction is less than 1.
Critical Vocabulary
Students will be skilled at …
S1 identifying prime and composite numbers using pictorial models including arrays.
S2 analyzing factor pairs to connect the concepts of prime and composite numbers.
S3 generating equivalent fractions.
S4 using models and objects to represent and solve problems involving addition and subtraction of fractions.
S5 applying properties of operations when adding or subtracting fractions with unequal denominators.
S6 estimating sums and differences of fractions using tools like number lines and benchmark numbers (0,12, 1).
S7 fluently adding and subtracting positive rational numbers (decimals and/or fractions).
S8 representing and solving problems involving multiplication of a whole number and a fraction using objects, pictorial models, and number lines.
S9 representing and solving problems involving division of a unit fraction by a whole number using objects, pictorial models, and number lines.
S10 representing and solving problems involving division of a whole number by a unit fraction using objects, pictorial models, and number lines.
S11 interpreting a remainder in a problem context.
S12 adding/subtracting decimals and fractions in the same problem by converting the numbers to the same form in order to solve the problem.
S13 applying the mathematical process standards.
TEKS
5.1 (A-G) The student uses mathematical processes to acquire and demonstrate mathematical understanding.
5.3 Numbers and Operations. The student applies mathematical process standards to develop and use strategies and methods for positive rational number computations in order to solve problems with efficiency and accuracy.
(A) estimate to determine solutions to mathematical and real-world problems involving addition, subtraction, multiplication, or division.
(H) represent and solve addition and subtraction of fractions with unequal denominators referring to the same whole using objects and pictorial models and properties of operations
(I) represent and solve multiplication of a whole number and a fraction that refers to the same whole using objects and pictorial models, including area models
(J) represent division of a unit fraction by a whole number and the division of a whole number by a unit fraction such as 1/3 ÷ 7 and 7 ÷ 1/3 using objects and pictorial models, including area models
(K) add and subtract positive rational numbers fluently
(L) divide whole numbers by unit fractions and unit fractions by whole numbers
5.4 Algebraic Reasoning. The student applies mathematical process standards to develop concepts of expressions and equations.
(A) identify prime and composite numbers
Texas Focal Point 1: Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
Bold = Readiness Standard