Operation Meanings/Relationships & Chance - Representing Division and Probability
During this block, students study the meaning and models of division. Particular emphasis should be placed on the inverse relationship
between multiplication and division and the two models of division (partitive, or ‘sharing’, and quotitive, or ‘repeated subtraction’).

Students experiment with outcomes of probability.

Utah State Core Standards, Objectives & Indicators

Standard 1: Students will understand the base-ten numeration system, place value concepts, simple fractions and perform operations with whole numbers.

Objective 3: Model problems involving addition, subtraction, multiplication, and division.

a. Demonstrate the meaning of multiplication and division of whole numbers through the use of a variety of representations (e.g., equal-sized groups, arrays, area models, and equal jumps on a number line for multiplication, partitioning and sharing for division).

b. Use a variety of strategies and tools, such as repeated addition or subtraction, equal jumps on the number line, and counters arranged in arrays to model multiplication and division problems.

Objective 4: Compute and solve problems involving addition and subtraction of 3- and 4-digit numbers and basic facts of multiplication and division.

c. Compute basic multiplication facts (0-10) and related division facts using a variety of strategies based on properties of addition and multiplication (i.e., commutative, associative, identity, zero, and the distributive properties).

Standard 2: Students will use patterns, symbols, operations, and properties of addition and multiplication to represent and describe simple number relationships.

Objective 2: Recognize, represent, and simplify simple number relationships using symbols, operations, and properties.

a. Represent numerical relationships as expressions, equations, and inequalities.

Standard 5: Students will collect and organize data to make predictions and identify basic concepts of probability.

Objective 2: Identify basic concepts of probability. a. Describe the results of events using the terms “certain,” “likely,” “unlikely,” and “impossible.”

b. Conduct simple probability experiments, record possible outcomes systematically, and display results in an organized way (e.g., chart, graph).c. Use results of simple probability experiments to describe the likelihood of a specific outcome in the future.

Core Vocabulary: divisor, dividend, quotient, likely, certain, outcome, impossible outcome