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My Math 4 Volume 2 Common Core, Grade: 4 Publisher: McGraw-Hill

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Metric Measurement And Area Models

An Introduction to Tenths

Once they attain fluency in fractions, fourth-graders move on to learn decimals. The introductory lessons focus on learning the tenths, which includes learning how to write and model whole numbers with tenths.

Learning decimals can be a bumpy road for many children, which is even more important to properly grasp early concepts, such as tenths, from the beginning. To help out in teaching this topic, we’ve outlined some cool teaching tips in this article. Read on to learn more.

How to Teach Tenths

Review place value.

Since understanding tenths builds on understanding the concept of place value, a good starting point for teaching this lesson can be reviewing children’s knowledge of place value. You can simply do a brief bell-work activity in order to do this.

For example, you can decide to write a few numbers on the whiteboard and ask whether the children can identify the place value of each digit. You may also want to check out our article on place value for additional activities and guidelines on this topic.

Define Tenths

Explain to students that in order to separate the whole number part from the fractional part, we use a decimal point, which is simply a dot. Point out that if a number has at least one digit to the right of the decimal point, we call it a decimal.

Define tenths as the first digit to the right of the decimal point. This digit shows the number of tenths. You can provide a few examples. For instance, explain that one part out of ten equal parts is the same as one tenth, or if we write it as a fraction, we’ll write 0.1.

A practical way to help children understand this is to draw a rectangle on the whiteboard and divide it into ten equal parts. Then, you can shade one part of the rectangle to illustrate one tenth or 0.1 in a visual way. For instance:

0.1 = one tenth

Another way to help students visualize one tenth is to draw a number line on the whiteboard and show where we can graph 0.1 on the number line, for example:

You can provide several examples, starting with smaller decimals and moving on to bigger ones, such as 0.3, 0.9, 1.2, 2.3, 7.2, 25.2, etc.

Reading Decimals

Even if they understand the basic principle of how to graph a decimal on the number line or how to present it visually, some children may struggle with reading the given decimal. So make sure you cover this area and provide examples of how we read or write decimals in word form.

For instance, point out that we read 0.3 as three tenths, 0.5 as five tenths, 1.2 as one and two tenths, 2.8 as two and eight tenths, 5.7 as five and seven tenths, etc. Then you can provide examples of bigger numbers, such as 285.2 or two hundred eighty-five and two tenths.

Additional Resources

You can also complement your lesson with a video presentation if you have the technical means in your classroom. For example, you can use this free video by Khan Academy to show children how to identify tenths on a number line.

Activities for Practice

Matching decimal game.

To play the matching decimal game, you’ll need to prepare two sets of decimal cards. The first set of cards contains decimals in a numerical form, such as 1.2 (one decimal per card), while the second set of cards contains the word form of a decimal, such as one and two tenths.

Make sure that there is a matching decimal card for each word decimal card. You can create twenty cards per group, that is, ten cards per set. You may also choose to laminate the cards. It may seem a bit time-consuming, but the beauty of the game is that you can reuse the cards each year.

Divide students into groups of 3 or 4 and hand out the two sets of cards to each group. The cards remain face down until you say it’s okay to play. Explain the rules of the game. The members of each group work together to quickly match the numerical with the word decimal cards.

This is a game that will challenge students to think fast and work fast, so it’s advisable that they already have a decent knowledge of tenths to be able to play it. The first group that manages to match all the cards, shouts: “decimal match”. If their answers are correct, they win the game.

Shaded Decimal Game

This is a fun online game that will help students reinforce their understanding of tenths with the help of visual models. Students are asked diverse decimal questions involving shaded models, for instance, to identify which decimal is shown by a shaded visual square or rectangle.

Divide students into pairs. Explain that they’ll play a game where they will compete against the other student in the pair by answering several questions on decimals. If they answer correctly, they score coins. They can also use a ‘hint’ from the game if they get stuck on a question.

In the end, the two students in each pair compare the number of coins they’ve scored. The person with the most coins is the winner of the game. Homeschooling parents can easily adjust this game and let their children play individually.

Tenths on the Number Line

This activity will help students practice their knowledge of tenths by graphing them on a number line. To implement this activity in your classroom, you’ll need a few large sheets of construction paper, markers, and a fraction worksheet.

Draw a number line on each cardboard paper (one per group depending on the size of the class). Then, move on to creating the worksheets with fractions. You can write ten fractions per worksheet. Just make sure the fractions are suitable and can be represented on the number line (ex: 0.9, 3.2, 1.4, etc.).

Divide students into groups of 3 or 4. Arrange the tables in the way that they form one large table so that they can place the construction paper on it and work together. Each group gets one construction paper, markers, and a fraction worksheet.

Provide instructions to students. Explain that this is not a competition, but simply an activity to practice graphing fractions on a number line. All members of a group should work together to correctly graph the fractions from their worksheets on their number line.

Provide a few minutes for this activity. After each group is done, they present their number line in front of the whole class. You can also decide to hang the number lines with fractions on the walls of the classroom in the end.

Before You Leave…

If you enjoyed these tips and activities, make sure to have a look at our whole lesson on teaching tenths to 4th graders! So if you need guidance to structure your class and teach it, sign up for our emails for more free lessons and content!

Feel free to also check out our blog – you’ll find plenty of awesome resources that you can use in your class! And if you’re ready to become a member, you can simply join us in the Math Teacher Coach community!

This article is based on:

Unit 6 – Decimal Fractions

• 6-2 Hundredths
• 6-3 Fractions to Decimals and Decimals to Fractions
• 6-4 Comparing and Ordering Decimals
• 6-5 Addition with Tenths and Hundredths
• 6-6 Money as Decimal Numbers

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Home > CC2 > Chapter 2 > Lesson 2.1.1 > Problem 2-8

How many tenths are in one whole? How many hundredths?  

Think of the question this way: What times one tenth equals one? What times one hundredth equals one?

You can also look at the root of the words. What word is in tenth and what word is in hundredth?

© 2022 CPM Educational Program. All rights reserved.

Count tenths in different ways

I can count tenths in different ways.

Lesson details

Key learning points.

• Tenths can be counted and represented with place value resources.
• Tenths can be counted and represented as decimals on a number line.
• Tenths can be counted and represented as fractions on a number line.

Common misconception

Recording ten tenths as 0.10 rather than 1 or 1.0

Be sure to address this regularly with pupils whilst counting. Demonstrate the regrouping using place value counters to help.

Decimal number - A decimal number has a decimal point followed by digits that show the fractional part.

Decimal point - A decimal point is a small dot used in a number to separate the whole number from the fractional part.

This content is © Oak National Academy Limited ( 2024 ), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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McGraw Hill My Math Grade 5 Chapter 6 Lesson 12 Answer Key Use Models to Divide Decimals

All the solutions provided in  McGraw Hill My Math Grade 5 Answer Key PDF Chapter 6 Lesson 12 Use Models to Divide Decimals  will give you a clear idea of the concepts.

McGraw-Hill My Math Grade 5 Answer Key Chapter 6 Lesson 12 Use Models to Divide Decimals

You can use models to divide decimals by decimals.

How many groups of 8 tenths are in 2.4? Find 2.4 ÷ 0.8.

2. Since you are dividing by tenths, replace both of the wholes with tenths. Each whole equals how many tenths? _____________ How many tenths do you have altogether after replacing the two wholes with tenths? ____________ Answer: 3 tenths. Explanation: Since we are dividing by tenths, replace both of the wholes with tenths. Each whole equals how many tenths 3 Separate the tenths into groups of eight tenths to show dividing by 0.8.

How many groups of 6 hundredths are in 3 tenths? Find 0.3 ÷ 0.06.

Talk About It

Use models to find each quotient. Draw the equal groups.

Question 5. 0.1 ÷ 0.05 = ______________ Answer: 2 Explanation: Given, 0.1 ÷ 0.05 = 2 Multiply both sides with 100. 0.05 x 100 = 5 0.1 x 100 = 10 10 ÷ 5 = 2

Question 6. 0.2 ÷ 0.04 = ______________ Answer: 5 Explanation: Given, 0.2 ÷ 0.04 Multiply both sides with 100. 0.2 x 100 =20 0.04 x 100 = 4 20 ÷ 4 = 5

Question 7. 0.27 ÷ 0.03 = ______________ Answer: 9 Explanation: Given, 0.27 ÷ 0.03 = 9 Multiply both sides with 100. 0.27 x 100 = 27 0.03 x 100 = 3 27 ÷ 3 = 9

Question 8. Mathematical PRACTICE Use Math Tools Grace purchased some packages of gum for $1.50. If each package costs $0.50, how many packages did Grace purchase? Use models to help you divide. Answer: 3 packages. Explanation: Grace purchased some packages of gum for $1.50. If each package costs $0.50, Total packages did Grace purchase, $1.50 ÷ $0.50 Multiply both sides with 100. 1.50 x 100 = 15 0.50 x 100 = 5 15 ÷ 5 = 3

Question 9. Aidan purchased 1.5 feet of wood to make a napkin holder. If he used 0.5 foot of wood for each side, how many sides does the napkin holder have? Use models to help you divide. Answer: 3 sides. Explanation: Aidan purchased 1.5 feet of wood to make a napkin holder. If he used 0.5 foot of wood for each side, Number of sides does the napkin holder have, 1.5 ÷ 0.5 Multiply both sides with 10. 1.5 x 10 = 15 0.5 x 10 = 5 15 ÷ 5 = 3

Question 11. Mathematical PRACTICE Explain to a Friend Explain how to use models to divide 2.1 by 0.7. Answer: 3 Explanation: To divide decimals using models, first shade in the first number, your dividend. Then, circle groups of the second number, your divisor. The number of circled groups is your answer, or quotient. 2.1 ÷ 0.7 There are 7 groups. So,  2.1 ÷ 0.7 = 3.

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McGraw Hill My Math Grade 5 Chapter 6 Lesson 12 My Homework Answer Key

Question 1. 0.4 ÷ 0.05 = _____________ Answer: 8 Explanation: 0.4 x 100 = 40 0.05 x 100 = 5 40 ÷ 5 = 8 8 x 0.05 = 0.4

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