Unit 2: Multiplication and Division of Whole Numbers and Decimals
Topics 3, 4, 5 & 6 in enVision; see Pearson app at webesk.pisd.edu
Students will understand that…
U1 There are multiple strategies and methods for finding an accurate mathematical solution.
U2 The relationship among the operations and their properties increases their flexibility as mathematicians.
U3 The context and numbers determine the strategies used to make estimations.
Students will know …
K1 multiplication and division are inverse operations.
K2 decimal numeration is just an extension of whole number place value.
K3 fractions and decimals describe quantities less than one whole.
K4 a variety of strategies for finding products and quotients based upon place value and properties of operations (including the distributive property).
K5 multiplication and division problems can be represented using models and pictures.
K6 products and quotients can be estimated using a variety of strategies such as front end estimation, compatible numbers, rounding up or down, or compensation.
K7 the standard algorithm used for dividing decimals is an extension of the standard algorithm for dividing whole numbers.
Critical Vocabulary
Students will be skilled at …
S1 using the relationship between multiplication and division to solve problems.
S2 modeling multiplication and division problems involving whole numbers using objects, pictorial models (area models), and strip diagrams.
S3 modeling multiplication problems involving decimals using objects, pictorial models, and area models (on hundredths grids) when used to represent a whole number times a decimal, a decimal times a decimal, and a mixed number times a mixed number.
S4 solving up to a four-digit dividend and a two-digit whole number divisor.
S5 solving for quotients to the hundredths with whole number divisors.
S6 recognizing patterns when dividing by a power of 10 and that the decimal point moves to the left when dividing by a power of 10.
S7 using strategies including mental math, place value, partial products, and properties of operations to solve multiplication and division problems.
S8 using the standard algorithm to solve multiplication and division problems involving whole numbers and decimals.
S9 evaluating solutions for reasonableness using estimation strategies.
S10 solving multi-step problems based on everyday situations.
S11 interpreting the remainder in a division problem.
S12 applying the mathematical process standards.
TEKS
5.1 (A-G) The student uses mathematical processes to acquire and demonstrate mathematical understanding.
5.3 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
(B) multiply with fluency a three-digit number by a two-digit number using the standard algorithm
(C) solve with proficiency for quotients of up to a four-digit dividend by a two-digit divisor using strategies and the standard algorithm
(D) represent multiplication of decimals with products to the hundredths using objects and pictorial models
(E) solve for products of decimals to the hundredths, including situations involving money, using strategies based on place-value understandings, properties of operations and the relationship to the multiplication of whole numbers
(F) represent quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using objects and pictorial models, including area models
(G) solve for quotients of decimals to the hundredths, up to four-digit dividends and two-digit whole number divisors, using strategies and algorithms, including the standard algorithm
Texas Focal Point 1: Developing an understanding of and fluency with addition, subtraction, multiplication, and division of fractions and decimals
Bold = Readiness Standard