Embedded Files
Investigation 1: Matching Operations and Questions + Reviewing Ratios and Rates
This Investigation has three Problems; however, we will be specifically focusing on two of them. The Problems help students recognize problem structures that lead to certain operations in given situations. Students also work to understand unit rates as expressions of ratios. While the remainder of the Unit requires that students use algorithms to compute with decimals, this Investigation focuses on helping students understand decimal numbers and how these numbers might be applied in real-world situations. Because of this, students should have access to scientific calculators to perform the arithmetic. They should also be able to explain which operations would help them solve the word problem.
In Problem 1.1, students enhance and test their abilities to recognize when each basic arithmetic operation is appropriate for solving problems. Students identify when addition, subtraction, multiplication, or division of decimals will answer the question(s) posed. In some cases, a combination of two or more operations is needed.
Problem 1.3 addresses unit rates and their connection to ratios. Students work with decimal numbers to find and scale unit rates. They continue to build their understanding of operations with decimals as they work through real-world problems.
Investigation 2: Adding and Subtracting Decimals
This Investigation has three Problems. We will be reviewing ideas of place value for decimals (from Comparing Bits and Pieces) as a class by breaking down decimals and making meaning out of each value.
In Problem 2.1, we will begin with learning how to expand decimals in a form that uses fractions. This expanded form serves as an explicit representation of place value, which will be revisited later in the Unit for the division algorithm. Afterwards, students will analyze student work given in the book and develop a standard algorithm for adding decimals. Problem 2.2 uses a similar structure to develop a standard algorithm for subtraction of decimals, so students will be referring back to the previous lesson to recognize this pattern.
Problem 2.3 brings back the idea of addition and subtraction fact families, in which students examine fact-family relationships. These fact-family relationships are designed to be an early introduction to algebra.
Investigation 3: Multiplying and Dividing Decimals
This Investigation has five Problems; however, we will be specifically focusing on Problem 3.1 and 3.3-5.
Problem 3.1 leads students to develop an algorithm for multiplying decimals with aid of, at most, paper and pencil. Problem 3.3 leads students in the same way as the previous Problem, except they will be developing an algorithm for dividing decimals. Problem 3.4 and Problem 3.5 review and extend student understanding and skill in division of multidigit whole numbers and connect this to multidigit division of decimals. The goal of this Investigation is to provide guidance for students to make sense of these standard algorithms.
Investigation 4: Using Percents
This Investigation has four Problems; however, we will be focusing on the first three only. The first three Problems deal with applications of percents as taxes, gratuities, and discounts—one application in each Problem.
Percent bars, also called tape diagrams, are useful in picturing relationships and in writing and solving mathematical sentences. Fact families again come into play in the service of rewriting sentences to find an unknown quantity.
Throughout this Investigation, we assume that students have access to at least a scientific calculator to perform the arithmetic. The focus is on the recognition of problem structures that lead to various operations on percents and decimals.
In all the Problems of this Investigation, students are asked three fundamental questions about percents: (1) What is a given percent of some base quantity? (2) What is the base quantity if a percent increase or decrease (as rate and amount) is known? and (3) How can a given increase or decrease in a quantity be expressed as a percent?
Link to our slide show Decimal Ops
To log in to the online version of your math text book, use these directions: CMP3 online
IXL: For extra practice students may visit ixl.com and login with their assigned credentials.
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