Help beginning students understand the connection between decimals and fractions with these concrete exercises using place value blocks and fraction grids.

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### Introduction and Objectives

Fractions can be a very tricky subject for many students. Usually, the best cure for fraction confusion is practice with concrete items. Sandwiches can be divided into halves, apples can be cut into fourths, pizzas can divided into eighths. However, it can be tough to practice fractions with denominators larger than ten using real items divided into pieces. The next best way to practice is with a clear picture, such as a square divided into hundredths. Use a blank ten by ten grid to help your students understand tenths and hundredths fractions more fully, and to provide the needed practice with this difficult subject.

In this lesson,

- Students will match tenths and hundredths fractions with a grid.
- Students will name fractions shown on the grid.
- Students will color a grid to match given fractions.

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### Supplies and Opening Activities

Gather the following supplies for this lesson:

- white board/markers/eraser.
- place value cubes that interconnect to form units, 10s and 100s.
- paper and pencil for each student.
- duplicated 10 and 100 grids for each student.
- duplicated fraction grid worksheets.

Introduce the lesson:

Begin by reviewing fraction and decimal concepts as needed with your group. Be sure everyone has the prerequisite knowledge, such as understanding of the vocabulary terms 'fraction,' 'numerator,' and 'denominator,' as well as decimal place value to the hundredths place. Students should be confident that the denominator tells how many sections are in the whole object or group, and that the numerator tells how many sections are being considered. They should also understand how to rename fractions both with concrete manipulatives and with number sentences. Students should also be familiar with place value cubes and how to manipulate them.

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### Lesson Activities

- Provide students with ten ten-unit place value sticks, connected to form a 100-unit sheet. Have student volunteers explain what this represents in terms of whole numbers. Student should be able to state that the blocks show that ten sets of ten units can be grouped to form a one hundred. Ask what will happen if they think of the 100-block as a single unit, then break the sticks apart. What portion of the 100-block is each stick? Guide the discussion to the fact that each stick represents one tenth of the 100-block. Practice creating tenth fractions with varying numbers of sticks connected together. Write these as fractions and decimals on the board.
- Provide each student with duplicated sheets of 10-grids. Challenge them to create fractions using their blocks, then sketch the same fraction on a 10-grid and name it as a tenths fraction and a tenths decimal. Allow time to practice as you circulate to check their work and understanding.
- Repeat the sequence, this time considering the single unit blocks that make up the 100-unit sheet (separate the sticks into their component units). Practice creating hundredth fractions, first with the place value blocks, then on the 100-grids on paper. Be sure to name each as a fraction and a decimal.

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### Evaluation and Follow-Up

Evaluate students' understanding using a worksheet that contains blank 10- and 100-grids with fractions to be colored, as well as completed grids with fractions to be identified. Make sure that each student understands the relationship between tenths/hundredths decimals and tenths/hundredths fractions. Suggested mastery level for this activity is 90%. Use the worksheet activity to identify students who need additional assistance and further practice.