Essential Questions: What is a decimal?
Why is it important to understand the relationship between fractions and decimals?
Why do we use different forms of numbers to represent equivalent values?
How will my understanding of whole numbers and fractions help me understand and use decimals when solving problems?
How can we use decimals to compare and compute fractional values?
How does my understanding of whole number operations help me develop my understanding of decimal operations?
Lesson Plan C.5: Use Decimal Notation for Fractions with Denominators of 10 or 100
Lesson Seed C.7: Compare Decimals
Lesson Seed C.5: Adding Decimal Fraction
Content Emphasis By Clusters in Grade 4
Progressions from Common Core State Standards in Mathematics
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Lesson seeds are ideas that can be used to build a lesson aligned to the CCSS. Lesson seeds are not meant to be all-inclusive, nor are they substitutes for instruction. When developing lessons from these seeds, teachers must consider the needs of all learners. It is also important to build checkpoints into the lessons where appropriate formative assessment will inform a teachers instructional pacing and delivery.
This unit introduces the concept of decimals for the first time. It is important for students in grade 4 to have a full understanding of our number Hindu-Arabic number system. This system is a collection of properties and symbols that results in a systematic way to way to write all numbers. This system is a positional decimal system, using symbols call digits for the ten values 0,1,2,3,4,5,6,7,8, and 9 to represent any number, no matter how large or small in quantity. The position of each digit within a number denotes the multiplier (power of ten) multiplied with that digit—each position has a value ten times that of the position to its right. Students apply their understanding of part-whole relationships (fractions) to partitioning numbers into groups based on powers of ten. They learn that by dividing one by ten, equals one tenth ( 1/10 ), one tenth divided by ten equals one hundredth 1/100. This understanding helps students understand decimal fractions. A decimal fraction is a fraction whose denominator is a power of ten. However decimals are expressed without a denominator, the decimal point, leading zeros (as needed) and the numerator corresponds to the power of ten of the denominator. For example 8/10 is written as 0.8, 8/100 is written as 0.83, etc. Students begin their work with decimals by expressing fractions with denominators of 10 or 100 in fraction form and then use this decimal form to add the fractions. For example, 3/10 + 24/100 can be represented as 30/100 + 24/100 = 54/100. Students use their knowledge of converting between dollars and cents to help them understand decimal fractions. After students demonstrate understanding of decimal fractions and the equivalency between fractions with tenths and hundredths, students can use the decimal fraction form to write equivalent decimal notation. They are able to make the connection between 30/100 + 24/100 = 54/100 to the decimal notation of 0.30 + 0.24 = 0.54.Students learn that any operation you can do with whole numbers, you can do with decimal fractions as an extension of the whole number system. This deep understanding of the entire number system helps student compare two decimals (to hundredths) by reasoning about their size. As with fractions, the comparison is only valid when the two decimals refer to the same whole or set. The Common Core assumes that by the end of sixth grade, students are fluent with operations related to fractions. The Common Core stresses the importance of moving from concrete fractional models to the representation of fractions using numbers and the number line. Concrete fractional models are an important initial component in developing the conceptual understanding of fractions. However, it is vital that we link these models to fraction numerals and representation on the number line. This movement from visual models to fractional numerals should be a gradual process as the student gains understanding of the meaning of fractions.
At the completion of the unit, the student will understand that:
Focus Standards (Listed as Examples of Opportunities for In-Depth Focus in the PARCC Content Framework document):
Possible Student Outcomes:
The student will be able to:
Evidence of Student Learning:
The Partnership for Assessment of Readiness for College and Careers (PARCC) has awarded the Dana Center a grant to develop the information for this component. This information will be provided at a later date. The Dana Center, located at the University of Texas in Austin, encourages high academic standards in mathematics by working in partnership with local, state, and national education entities. Educators at the Center collaborate with their partners to help school systems nurture students' intellectual passions. The Center advocates for every student leaving school prepared for success in postsecondary education and in the contemporary workplace.
Fluency Expectations and Examples of Culminating Standards:
Sample Assessment Items: The items included in this component will be aligned to the standards in the unit and will include:
Interventions/Enrichments/PD: (Standard-specific modules that focus on student interventions/enrichments and on professional development for teachers will be included later, as available from the vendor(s) producing the modules.)
Vocabulary/Terminology/Concepts: This section of the Unit Plan is divided into two parts. Part I contains vocabulary and terminology from standards that comprise the cluster, which is the focus of this unit plan. Part II contains vocabulary and terminology from standards outside of the focus cluster. These “outside standards” provide important instructional connections to the focus cluster.
equivalent fractions: two or more fractions that have the same value.
Example # 2: What fraction of dots are shaded, if the whole is represented by all the black and white dots in the entire rectangle?
Part II – Instructional Connections outside the Focus Cluster
visual fraction model: a model that shows operations or properties of fractions using pictures.
decimal: a fraction with an unwritten denominator of 10 or some power of 10, indicated by a point (.) before the numerator.
decompose: breaking a number into two or more parts to make it easier with which to work.
Relevant Grade 3 Vocabulary:
whole: In fractions, the whole refers to the entire region, set, or line segment which is divided into equal parts or segments.
numerator: the number above the fraction bar; names the number of parts of a region or set being referenced.
Example: A week has 7 days. The weekend represents 2/7 of a week. The 2 is the numerator which tells the number of days in a weekend.
denominator: the number below the fraction bar; states the total number of parts in the region or set.
Example: A week has 7 days. The weekend represents 2/7 of a week. The 7 is the denominator which tells the total number of days in a week.
fraction of a region: is a number which names a part of a whole area.
Shaded area represents 4/24 or 1/6 of the region
linear models: used to perform operations with fractions and identify their placement on a number line. Some examples are fraction strips, fraction towers, Cuisenaire rods, number line and equivalency tables.
equivalent fractions: different fractions that name the same part of a region, part of a set, or part of a line segment.
benchmark fraction: fractions that are commonly used for estimation or for comparing other fractions.
Example: Is 2/3 greater or less than 1/2?
improper fraction: a fraction in which the numerator is greater than or equal to the denominator.
mixed number: a number that has a whole number and a fraction.