Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100. 4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.* For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100. 4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram. 4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model. *Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
Anchor Standard/Mathematical Practice(s)
MP.2. Reason abstractly and quantitatively. MP.4. Model with mathematics. MP.5. Use appropriate tools strategically. MP.7. Look for and make use of structure.
Information Technology Standard
Use technology tools and skills to reinforce classroom concepts and activities.
Revised Bloom's Level of thinking
Understanding Applying Evaluating Creating
Learning Target/Task Analysis
4.NF.5 This standard continues the work of equivalent fractions by having students change fractions with a 10 in the denominator into equivalent fractions that have a 100 in the denominator. In order to prepare for work with decimals (4.NF.6 and 4.NF.7), experiences that allow students to shade decimal grids (10x10 grids) can support this work. Student experiences should focus on working with grids rather than algorithms. Students can also use base ten blocks and other place value models to explore the relationship between fractions with denominators of 10 and denominators of 100. This work in fourth grade lays the foundation for performing operations with decimal numbers in fifth grade. 4.NF.6 Students make connections between fractions with denominators of 10 and 100 and the place value chart. By reading fraction names, students say 32/100 as thirty-two hundredths and rewrite this as 0.32 or represent it on a place value model as shown below. see Common Core Flipbook p.46 Students use the representations explored in 4.NF.5 to understand 32/100 can be expanded to 3/10 and 2/100. Students represent values such as 0.32 or 32/100 on a number line. 32/100 is more than 30/100 (or 3/10) and less than 40/100 (or 4/10). It is closer to 30/100 so it would be placed on the number line near that value. 4.NF.7 Students build area and other models to compare decimals. Through these experiences and their work with fraction models, they build the understanding that comparisons between decimals or fractions are only valid when the whole is the same for both cases.
I can...
I can restate fractions that have a denominator of 10 or 100 as equvalent. (3/10=30/100)
I can explain the relationship between tenths and hundredths.
I can add two fractions that have a denominator of 10 or 100. (3/10 + 4/100=34/100)
I can convert decimals into fractions, with denominators of 10 or 100.
I can convert fractions into decimals, with denominators of 10 or 100.
I can compare two decimals up to the hundredths place.
Essential Vocabulary
compare, decimals, hundredths, tenths, symbols
Sample Assessments
Model tenths and hundredths using dimes (1/10) and pennies (1/100), 10 x 10 grid, meter stick, etc. to illustrate the use of common denominators. Use a 10 x 10 grid to demonstrate addition of 7/10 + 6/100. Explain why the fractions can be added as they are when using the grid, but when writing out the equation they must have a common denominator. 5/10 =a/100 70/100 =b/10 2/10 + 40/100 = c Compare 1. 0.1 and 0.7 2. 1.2 and 2.1 3. 0.3 and 0.30 4. 0.5 and 0.05 5. 0.4 and 0.17
Ron says 0.17 is greater than 0.4. Kym says Ron is wrong. Who is right? Justify your answer with written explanation and a visual model.
Develop a model to describe the addition of 7/10 + 3/100.
Instructional Resources
Link to students’ background knowledge of place value where the value of each place is ten times the value of the place to its immediate right in order to extend the pattern to decimal place value. When comparing two decimals, remind students that, as in comparing two fractions, the decimals need to refer to the same whole. Allow students to use visual models to compare two decimals. They can shade in a representation of each decimal on a 10 x 10 grid. The 10 x 10 grid is defined as one whole. The decimal must relate to the whole.
Common Core Standards
Grade 4 expectations in this domain are limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, 100.4.NF.5. Express a fraction with denominator 10 as an equivalent fraction with denominator 100, and use this technique to add two fractions with respective denominators 10 and 100.* For example, express 3/10 as 30/100, and add 3/10 + 4/100 = 34/100.
4.NF.6. Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.
4.NF.7. Compare two decimals to hundredths by reasoning about their size. Recognize that comparisons are valid only when the two decimals refer to the same whole. Record the results of comparisons with the symbols >, =, or <, and justify the conclusions, e.g., by using a visual model.
*Students who can generate equivalent fractions can develop strategies for adding fractions with unlike denominators in general. But addition and subtraction with unlike denominators in general is not a requirement at this grade.
Anchor Standard/Mathematical Practice(s)
MP.2. Reason abstractly and quantitatively.MP.4. Model with mathematics.
MP.5. Use appropriate tools strategically.
MP.7. Look for and make use of structure.
Information Technology Standard
Use technology tools and skills to reinforce classroom concepts and activities.Revised Bloom's Level of thinking
UnderstandingApplying
Evaluating
Creating
Learning Target/Task Analysis
4.NF.5This standard continues the work of equivalent fractions by having students change fractions with a 10 in
the denominator into equivalent fractions that have a 100 in the denominator. In order to prepare for
work with decimals (4.NF.6 and 4.NF.7), experiences that allow students to shade decimal grids (10x10
grids) can support this work. Student experiences should focus on working with grids rather than
algorithms. Students can also use base ten blocks and other place value models to explore the
relationship between fractions with denominators of 10 and denominators of 100.
This work in fourth grade lays the foundation for performing operations with decimal numbers in fifth
grade.
4.NF.6
Students make connections between fractions with denominators of 10 and 100 and the place value chart.
By reading fraction names, students say 32/100 as thirty-two hundredths and rewrite this as 0.32 or
represent it on a place value model as shown below.
see Common Core Flipbook p.46
Students use the representations explored in 4.NF.5 to understand 32/100 can be expanded to 3/10 and
2/100.
Students represent values such as 0.32 or 32/100 on a number line. 32/100 is more than 30/100 (or 3/10)
and less than 40/100 (or 4/10). It is closer to 30/100 so it would be placed on the number line near that
value.
4.NF.7
Students build area and other models to compare decimals. Through these experiences and their
work with fraction models, they build the understanding that comparisons between decimals or
fractions are only valid when the whole is the same for both cases.
I can...
I can restate fractions that have a denominator of 10 or 100 as equvalent. (3/10=30/100)
I can explain the relationship between tenths and hundredths.
I can add two fractions that have a denominator of 10 or 100. (3/10 + 4/100=34/100)
I can convert decimals into fractions, with denominators of 10 or 100.
I can convert fractions into decimals, with denominators of 10 or 100.
I can compare two decimals up to the hundredths place.
Essential Vocabulary
compare, decimals, hundredths, tenths, symbols
Sample Assessments
Model tenths and hundredths using dimes (1/10) and pennies (1/100), 10 x 10 grid, meter stick, etc. to illustrate the use of common denominators.Use a 10 x 10 grid to demonstrate addition of 7/10 + 6/100. Explain why the fractions can be added as they are when using the grid, but when writing out the equation they must have a common denominator.
5/10 =a/100
70/100 =b/10
2/10 + 40/100 = c
Compare
1. 0.1 and 0.7
2. 1.2 and 2.1
3. 0.3 and 0.30
4. 0.5 and 0.05
5. 0.4 and 0.17
Ron says 0.17 is greater than 0.4. Kym says Ron is wrong. Who is right? Justify your answer with written explanation and a visual model.
Differentiation
Intervention:
http://daretodifferentiate.wikispaces.com/Choice+BoardsEnrichment:
Develop a model to describe the addition of 7/10 + 3/100.
Instructional Resources
Link to students’ background knowledge of place value where the value of each place is ten times the value of the place to its immediate right in order to extend the pattern to decimal place value.
When comparing two decimals, remind students that, as in comparing two fractions, the decimals need to refer to the same whole. Allow students to use visual models to compare two decimals. They can shade in a representation of each decimal on a 10 x 10 grid. The 10 x 10 grid is defined as one whole. The decimal must relate to the whole.
Notes and Additional Information