Unit 5

Decimal Fractions

Grade 4




In unit 5, students find equivalent fractions to change fractions with a denominator of 10 to a denominator of 100.  Students should recognize that decimal place value units are special fraction units:  0.7, 7 tenths, and  are different ways to show the same number.  Students will include decimal places on the place value chart.  Students will use base-ten blocks, grids, and number lines as the primary models for developing conceptual understanding.  Students will read and write decimal numbers to hundredths.

Students add and subtract tenths plus hundredths using models and visual representations.  Students add and subtract fractions with unlike units, for example, 3 tenths + 4 hundredths = 30 hundredths + 4 hundredths.  Students compare decimals using the symbols >, < and =.  Students will apply their understanding of decimal fractions to solve measurement word problems.

Louisiana Student Standards for Mathematics (LSSM)


Major Cluster: Number and Operations-Fractions

Understand decimal notations for fractions, and compare decimal fractions.




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.




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; represent 62/100 of a dollar as $0.62.



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.

Supporting Cluster:  Measurement and Data

Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit




Know relative sizes of measurement units within one system of units including ft, in, km, m, cm; kg, g; lb., oz.; l, ml; hr., min, sec.  Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. (Conversions are limited to one-step conversions.)  Record measurement equivalents in a two-column table.  For example, know that 1 ft. is 12 times as long as 1 in.  Express length of a 4 ft. snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ….





Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving whole numbers and/or simple fractions (addition and subtraction of fractions with like denominators and multiplying a fraction times a fraction or a whole number), and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale.

Note:  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.

Operations and Algebraic Thinking

Generate and analyze patterns.




Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself. For example, given the rule “Add and the starting number 1, generate terms in the resulting sequence and observe that the terms appear to alternate between odd and even numbers. Explain informally why the numbers will continue to alternate in this way






Enduring Understandings:


·         Fractions can be expressed as decimals.

•      Decimals can be represented visually and in written form.

•      Decimals are a part of the base ten system.

·         Comparisons of two decimals are only valid when the two decimals refer to the same whole.

Essential Questions:


·   What is a decimal fraction and how can it be represented?

• What patterns occur on a number line made up of decimal fractions?

·   When we compare two decimals, how do we know which has a greater value?

·   What is the relationship between fractions with denominators of 10 and denominators of 100?

·   How can I represent a fraction with a denominator of 10 on a hundreds grid?

·   How can I use what I know about decimal fractions to solve problems involving metric measurement?