Math Mammoth Decimals 1

45 pages
(answers included)

Sample pages (PDF)
Contents and Introduction
Two Decimal Digits: Hundredths
Decimals & Measuring Units
Using Mental Math with Money

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Este libro en español

Math Mammoth Decimals 1 is is a worktext about decimal numbers for approximately 3rd and 4th grade levels. Being a worktext, it includes both the instruction and the exercises, all written directly to the student.

This book deals with decimal numbers that have tenths and hundredths—numbers with a maximum of two decimal digits. We only deal with some of the basic operations: addition, subtraction, and multiplication by a whole number, with a strong emphasis on mental calculations. The idea is to lay a solid conceptual foundation so that the student does not succumb to rote memorization of rules and procedures without understanding.

Note: multiplication and division of decimals are not covered. Those are taught in Math Mammoth Decimals 2.

We start out with place value—first only with tenths, or numbers with one decimal digit, and in a later lesson with hundredths. The lessons use number lines, fraction models, and place value charts to teach decimal place value and comparing decimals.

Next, students add and subtract decimals, both in columns and using mental math. We compare decimal operations with corresponding fraction operations in order to show why they work.

A common student error is to add 0.4 + 0.8 = 0.12. Here, the student may be considering the decimal part of a number as a “separate whole number”, and try to apply whole number arithmetic within the decimal part. To help such a student, read the decimals as fractions and emphasize how fractions are added. Think: four tenths plus eight tenths equals twelve tenths, which is 1.2.

When we add decimals of different ”lengths“ (numbers with different amounts of decimal digits), such as 0.4 + 0.08, you can tag a zero to the end of 0.4 so the problem becomes 0.40 + 0.08. Now, both addends have hundredths, so the answer is simply 48 hundredths or 0.48. This is the same thing as converting the corresponding fractions (four tenths and eight hundredths) to have the same denominator (forty hundredths and eight hundredths).

As a real-life application, the book includes a lesson on using decimals with metric measurement units.

Lastly, while the focus of the book is on place value, addition, and subtraction, we also study some mental math techniques in the context of money. While the focus of the book is place value, addition, and subtraction, the book also covers some mental math techniques in the context of money. For example, to find 7 × $2.99, you can multiply 7 × $3 = $21, and then subtract seven cents, to get the total of $20.93.😁

The PDF version of this book can be filled in on a computer, phone, or tablet, using the annotation tools found in many PDF apps. See more.