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Chapter 17: Problem 1

List three different models that help support students' exploration of decimals.

Short Answer

Expert verified
Base ten blocks, number lines, and decimal grids support decimal exploration.

Step by step solution

01

Base Ten Blocks

Base ten blocks are physical models that consist of unit cubes (representing 0.1 or 0.01), rods or longs (representing 1.0 or 0.1), flats (representing 10.0 or 1.0), and sometimes larger pieces. These blocks help students visualize how decimals relate to whole numbers and understand operations with decimals by manipulating these physical objects.
02

Number Lines

A number line is a visual representation that can be used to demonstrate the placement of decimals between whole numbers. By marking points on a number line, students can better grasp the concept of decimal fractions, compare the size of decimals, and perform operations like addition and subtraction.
03

Decimal Grids

Decimal grids are diagrams that represent whole numbers divided into 10 or 100 equal parts. Each part corresponds to a decimal fraction of 0.1 or 0.01, respectively. These grids aid students in visualizing decimals as parts of a whole, making it easier to understand concepts such as decimal addition, subtraction, and equivalence.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Base Ten Blocks
Base ten blocks are wonderful hands-on tools to help students understand decimals. Imagine these blocks as real-life versions of math. They consist of different pieces, each representing decimal values. For instance, unit cubes typically stand for 0.1 or 0.01, while rods or longs are used to symbolize 1.0 or 0.1. Flats can represent either 10.0 or 1.0, providing flexibility in showing various decimal places.
These blocks allow students to physically manipulate and visualize decimals in relation to whole numbers.
  • They enable students to "see" decimals and how they fit together.
  • By building numbers with blocks, learners can explore how decimals operate in addition, subtraction, multiplication, and division.
Using base ten blocks makes mathematical operations with decimals interactive and tangible, making abstract concepts more concrete.
Number Lines
Number lines are a simple yet powerful visual tool for teaching decimals. This representation allows students to see where decimals fit between whole numbers. By marking decimals on a number line, learners gain a clear visual understanding of decimal fractions.
This method helps them:
  • Compare decimals from smallest to largest easily, spotting differences by observing their placements.
  • Understand decimal intervals and their relation to whole numbers.
  • Perform operations like addition and subtraction by "walking" between points on the line.
Number lines breathe life into numbers, enabling students to imagine decimals as part of a journey down a path.
Decimal Grids
Decimal grids break down numbers into easy-to-understand parts. These grids map out a whole number into either 10 or 100 equal segments. Each segment then represents a decimal fraction, such as 0.1 or 0.01 respectively.
Decimal grids allow students to:
  • Visualize how decimals are fractions of a whole.
  • Understand concepts like decimal addition and equivalency by coloring or shading parts of the grid.
  • Quickly grasp subtraction by removing a section of the grid.
By laying out numbers in grids, this method provides a clear graphical representation of how decimals add up to form whole numbers, making abstract concepts easier to grasp.

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Most popular questions from this chapter

Explain how the line-up-the-decimals rule for adding and subtracting can be developed through practice with estimation.

Explain how the line-up-the-decimals rule for adding and subtracting decimals can be developed through practice with estimation.
See all solutions

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