Students begin module 2 by using visual models and an understanding of divisibility to find the greatest common factor and least common multiple of pairs of numbers. Then, students apply their previous understanding of multiplication and division to divide fractions by fractions. They model fraction division expressions with tape diagrams and double number lines, use common denominators to divide fractions by fractions, and then develop and apply the invert and multiply strategy. Students use standard algorithms to fluently add, subtract, and multiply decimals, and apply those skills in real-world applications. They extend their understanding of division from prior grades to use the standard division algorithm to divide multi-digit numbers and decimals.
In topic A, students first explore visual models involving square and rectangular tiles to determine common factors and common multiples of pairs of numbers. Students learn strategies for determining divisibility by 3 and 6, use number sense to reason about divisibility of any given number, and explore the connection between divisibility and factors. They learn the definitions for greatest common factor (GCF) and least common multiple (LCM) and use a variety of strategies to find GCF and LCM, including organized lists of factors and multiples, prime factorization, and Venn diagrams. In an optional lesson, students learn and apply the Euclidean algorithm to find the GCF of two numbers and use the GCF to find the LCM.
In topic B, students divide fractions by whole numbers and whole numbers by fractions. They model fraction division with tape diagrams and number lines, reason about the relationship between multiplication and division, and interpret fraction division problems as number of groups unknown or group size unknown. At the end of the topic, students divide fractions by fractions by creating common denominators.
Topic C introduces the invert and multiply strategy for dividing fractions. Students use tape diagrams to reason about why the strategy works. Then they apply the strategy to fluently divide fractions and mixed numbers. Students use fraction division to solve real-world problems and make multiplicative comparisons. At the end of the topic, students add, subtract, multiply, and divide fractions in a real-world task involving designing wood box race cars.
In topic D, students fluently add, subtract, and multiply multi-digit decimals. First, students use number sense and place value reasoning to add and subtract decimals and determine the placement of the decimal point in sums and differences. Then students reason about the products of decimal factors and use the standard multiplication algorithm to efficiently multiply decimals. At the end of the topic, students apply these skills in a real-world task by calculating costs and revenue of a building project and adjusting their building model to try to increase profit.
In topic E, students extend their understanding of division and use the standard algorithm to fluently divide whole numbers. They reason about the size of the quotient and the placement of its decimal point by using place value reasoning, and they estimate to determine the reasonableness of their answers. Students also learn to express quotients as decimals and round quotients when needed.
In topic F, students extend their understanding of the standard division algorithm to fluently divide decimals. First, they divide decimals by whole numbers and then progress to dividing decimals by decimals and applying decimal division to solve multi-step real-world problems. At the end of the topic, students practice decimal division in a multi-step task involving calculations about resources needed to survive on Mars.