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K-8 Mathematics StandardsContent Training

Decimal Understanding

Cathey Bolson, Regional Math Coordinator, ESD 123

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Develop participant’s conceptual understanding of decimals.

Experience activities that help students develop decimal understanding.

Discover the level of understanding for decimals at your grade level based on the state standards.

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Allow ourselves and others to be seen as learners.

Monitor own airtime and sidebar conversations.

Allow for opportunities for equitable sharing.

Presume positive intentions.

Be respectful when giving and receiving opinions, ideas and approaches.

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For all students to learn significant mathematics, content should be taught and assessed in meaningful situations.

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Conceptual Understanding◦ Making sense of mathematics

Procedural Proficiency◦ Skills, facts, and procedures

Mathematical Processes◦ Using mathematics to reason and think

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At each grade level:◦ 3-4 Core Content areas◦ Additional Key Content◦ Core Processes (reasoning, problem solving, communication)

For each of these:◦ Overview paragraph◦ Performance Expectation◦ Comments/Examples

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Use either your Standards Document or Strands Document to find all K-8 references to decimals.

Go back and carefully read the Performance Expectations and Explanatory Comments and Examples for your grade level.

Note the expectations for the grade level above and below yours.

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What should your students already know?What do you need to teach this year?What do they need to know for next year?

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With a partner, use any of the materials

provided at your table, and make a

model of the number

1.55

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What mathematical understanding went into making your model?

What mathematical knowledge would students need to be able to complete this task?

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Students initial interaction with decimals will most likely be money and measurement. However, these SHOULDN’T be the only context used to introduce decimals. Students should understand that decimals are an extension of the base-ten place-value system.

Students understand decimal notation as an extension of the base-ten system of writing whole numbers that is useful for representing more numbers, including numbers between 0 and 1, between 1 and 2, and so on.(NCTM, Curricular Focal Points Grade 4)

Cut the grid paper on your table to make the number 143

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How would your model change if the unit was now the 10x10 square?

If the square is the unit, what are the longs? What are the small squares? What is the number now?

What convention do we need to define the unit?

How does grid paper relate to the base-ten blocks?

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Using base-ten blocks, model the number 0.34. REMEMBER – THE UNIT IS THE 10X10 SQUARE

What fraction is this?

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30 minutes

How does the grid number line compare to the previous models? How many grids are one unit?

Use your number lines to order the following numbers:

0.3, 0.56, 0.17, 0.42, 0.275

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Using the base-ten blocks (the square is the unit), create the number 0.13

Make sure you mark your decimal!!!

Multiply 0.13 by 10 (don’t remove the previous model)

What happened to the number?

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Students understanding and strategies for computing whole numbers should be used to develop their understanding for computation of decimals.

What are some strategies that could be used to teach addition and subtraction?

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Roll the die and use the unit cubes to create the numbers rolled.◦ Example: Lucy rolled a 0.5 and a 0.2, she would connect five

cubes together and then two cubes together and place them on her board.

Continue taking turns making stacks of the numbers rolled. After creating stacks, look at your “towers” to see if you have any number combinations that create a “1”. If so, create the combinations, and record the number sentence on your score sheet. The first person to create five “1’s” is the winner.

Make a chart like this on a piece of paper:

Tenth Hundredth Total

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The purpose of this activity is to help students partition decimal numbers in order to make addition easier.

The goal is to combine tenths to make one. In some cases you will need to decompose the number to make a one. Then add the remaining tenths and create a number sentence for the total amount of tenths within your figure.

Repeat, but try and make tenths by combining hundredths.

Don’t push this until students are ready.

Focus should be on ESTIMATION before any formal procedure is introduced.

Teach to line-up the numbers by place-value, not the decimal point.

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7.05 + 0.31 + 2.745

1. Estimate the answer2. Find the exact answer3. Find the exact answer using a different strategy

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Using base-ten blocks, model 0.3 x 1.3

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What challenges exist when creating this model?

What other models could be used?

On grid paper, create an array for:◦ 0.3 x 1.3

◦ 0.3 x 0.3

◦ 0.3 x 0.35

Which of these was the greatest challenge? How could you use this help students estimate

products?

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Compute the following product: 24 x 63

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Without computing the following products, give an exact answer to the following (DO NOT COUNT DECIMAL PLACES):

0.24 x 6.3 24 x 0.63 2.4 x 63 0.24 x 0.63

Solve each problem using multiplication only. Guess and check until you get the correct answer. The person with the least number of guesses wins!

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Solve: 4 x = 87 5 x = 106 8 x = 98

What are some multiplication strategies for whole-numbers?

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Doubles-Doubles-Doubles 2-4 players Roll the number cubes, and mentally compute

the product Place a marker on the board First person to place all four markers on the

board wins!!!

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About Teaching Mathematics, Marilyn Burns◦ www.mathsolutions.com

Teaching Student Centered Mathematics, Grades 3-5, John A. Van de Walle◦ www.ablongman.com

Fundamentals, ORIGO Education◦ www.origomath.com

Understanding Numbers: Decimals, Kathy Richardson◦ www.mathperspectives.com

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