All the resources on this page come from the GADOE Framework 4th Grade Unit 3 Overview. Reviewing this information before or during planning can help ensure your instruction is aligned with the standards and is at the depth expected.

Unit 3 Overview

In this unit students will:

● understand representations of simple equivalent fractions

● compare fractions with different numerators and different denominators

Although the units in this instructional framework emphasize key standards and big ideas at specific times of the year, routine topics such as estimation, mental computation, and basic computation facts should be addressed on an ongoing basis. Ideas related to the eight STANDARDS FOR MATHEMATICAL PRACTICE: making sense of problems and persevering in solving them, reasoning abstractly and quantitatively, constructing viable arguments and critiquing the reasoning of others, modeling mathematics, using appropriate tools strategically, attending to precision, looking for and making use of structure, and looking for and expressing regularity in repeated reasoning, should be addressed continually as well. The first unit should establish these routines, allowing students to gradually enhance their understanding of the concept of number and to develop computational proficiency. These tasks are not intended to be the sole source of instruction. They are representative of the kinds of experiences students will need in order to master the content, as well as mathematical practices that lead to conceptual understanding. Teachers should NOT do every task in the unit; they should choose the tasks that fit their students’ needs. The tasks in these units illustrate the types of learning activities that should be utilized from a variety of sources. For more detailed information about unpacking the content standards, unpacking a task, math routines and rituals, maintenance activities and more, please refer to the Grade Level Overview for Grade 4.

STANDARDS FOR MATHEMATICAL PRACTICE

This section provides examples of learning experiences for this unit that support the development of the proficiencies described in the Standards for Mathematical Practice. These proficiencies correspond to those developed through the Literacy Standards. The statements provided offer a few examples of connections between the Standards for Mathematical Practice and the Content Standards of this unit. This list is not exhaustive and will hopefully prompt further reflection and discussion.

1. Make sense of problems and persevere in solving them. Students make sense of problems involving equivalent fractions and comparing fractions.

2. Reason abstractly and quantitatively. Students demonstrate abstract reasoning about relative size of fractions.

3. Construct viable arguments and critique the reasoning of others. Students construct and critique arguments regarding the equivalency of fractions.

4. Model with mathematics. Students use constructed fraction strips to demonstrate understanding of equivalent fractions.

5. Use appropriate tools strategically. Students select and use tools such as fraction strips and number lines to identify equivalent fractions.

6. Attend to precision. Students attend to the language of real-world situations to determine if one fraction is greater than another.

7. Look for and make use of structure. Students relate the structure of fractions to the same whole to compare fractions.

8. Look for and express regularity in repeated reasoning. Students relate the structure of fractions to the same whole to identify multiple equivalent fractions.

***Mathematical Practices 1 and 6 should be evident in EVERY lesson. ***

STANDARDS FOR MATHEMATICAL CONTENT

Extend understanding of fraction equivalence and ordering.

MGSE4.NF.1 Explain why two or more fractions are equivalent 𝑎 𝑏 = 𝑛 × 𝑎 𝑛 × 𝑏 ex: 1 4 = 3 × 1 3 × 4 by using visual fraction models. Focus attention on how the number and size of the parts differ even though the fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.

MGSE4.NF.2 Compare two fractions with different numerators and different denominators, e.g., by using visual fraction models, by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1 2 . Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions.

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

MGSE4.MD.2 Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, 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

BIG IDEAS

• Fractions can be represented visually and in written form.

• Fractions with differing parts can be the same size.

• Fractions of the same whole can be compared.

• Fractions with the same amount of pieces can be compared using the size of their pieces.

• Fractions can be compared using benchmarks like 0, 1 2 and 1.

• Fraction relationships can be expressed using the symbols, >, <, or =.

ESSENTIAL QUESTIONS

Choose a few questions based on the needs of your students.

● What is a fraction and how can it be represented?

● How can equivalent fractions be identified?

● In what ways can we model equivalent fractions?

● How can identifying factors and multiples of denominators help to identify equivalent fractions?

● What are benchmark fractions?

● How are benchmark fractions helpful when comparing fractions?

● How can we use fair sharing to determine equivalent fractions?

● How do we know fractional parts are equivalent?

● What happens to the value of a fraction when the numerator and denominator are multiplied or divided by the same number?

● How are equivalent fractions related?

● How can you compare and order fractions?

● How do I compare fractions with unlike denominators?

● How do you know fractions are equivalent?

● What can you do to decide whether your answer is reasonable?

• How do we locate fractions on a number line?

CONCEPTS/SKILLS TO MAINTAIN

It is expected that students will have prior knowledge/experience related to the concepts and skills identified below. It may be necessary to pre-assess in order to determine if time needs to be spent on conceptual activities that help students develop a deeper understanding of these ideas.

● Identify and give multiple representations for the fractional parts of a whole (area model) or of a set, using halves, thirds, fourths, sixths, eighths, tenths and twelfths.

● Recognize and represent that the denominator determines the number of equally sized pieces that make up a whole.

● Recognize and represent that the numerator determines how many pieces of the whole are being referred to in the fraction.

● Compare fractions with denominators of 2, 3, 4, 6, 10, or 12 using concrete and pictorial models.

Fluency: Procedural fluency is defined as skill in carrying out procedures flexibly, accurately, efficiently, and appropriately. Fluent problem solving does not necessarily mean solving problems within a certain time limit, though there are reasonable limits on how long computation should take. Fluency is based on a deep understanding of quantity and number.

Deep Understanding: Teachers teach more than simply “how to get the answer” and instead support students’ ability to access concepts from a number of perspectives. Therefore, students are able to see math as more than a set of mnemonics or discrete procedures. Students demonstrate deep conceptual understanding of foundational mathematics concepts by applying them to new situations, as well as writing and speaking about their understanding.

Memorization: The rapid recall of arithmetic facts or mathematical procedures. Memorization is often confused with fluency and automaticity. Fluency implies a much richer kind of mathematical knowledge and experience. Number Sense: Students consider the context of a problem, look at the numbers in a problem, make a decision about which strategy would be most efficient in each particular problem. Number sense is not a deep understanding of a single strategy, but rather the ability to think flexibly between a variety of strategies in context.

Fluent students:

• flexibly use a combination of deep understanding, number sense, and memorization.

• are fluent in the necessary baseline functions in mathematics so that they are able to spend their thinking and processing time unpacking problems and making meaning from them.

• are able to articulate their reasoning.

• find solutions through a number of different paths.

For more about fluency, see: http://www.youcubed.org/wpcontent/uploads/2015/03/FluencyWithoutFear-2015.pdf and: https://bhi61nm2cr3mkdgk1dtaov18-wpengine.netdna-ssl.com/wp-content/uploads/nctm-timedtests.pdf

STRATEGIES FOR TEACHING AND LEARNING

● Students should be actively engaged by developing their own understanding.

● Mathematics should be represented in as many ways as possible by using graphs, tables, pictures, symbols, and words.

● Interdisciplinary and cross-curricular strategies should be used to reinforce and extend the learning activities.

● Appropriate manipulatives and technology should be used to enhance student learning.

● Students should be given opportunities to revise their work based on teacher feedback, peer feedback, and metacognition, which includes self-assessment and reflection.

● Students should write about the mathematical ideas and concepts they are learning.

● Books such as Fraction Action (2007) written and illustrated by Loreen Leedy and Working with Fractions (2007) by David A. Adler and illustrated by Edward Miller, are useful resources to have available for students to read during the instruction of these concepts.

● Consideration of all students should be made during the planning and instruction of this unit. Teachers need to consider the following:

● What level of support do my struggling students need in order to be successful with this unit?

● In what way can I deepen the understanding of those students who are competent in this unit?

● What real life connections can I make that will help my students utilize the skills practiced in this unit?

SELECTED TERMS AND SYMBOLS

Note – At the elementary level, different sources use different definitions. Please preview any website for alignment to the definitions given in the frameworks. Mathematics Standards Glossary of Mathematical Terms: http://www.corestandards.org/Math/Content/mathematicsglossary/glossary.

The terms below are for teacher reference only and are not to be memorized by the students. ● common fraction ● denominator ● equivalent sets ● increment ● numerator ● proper fraction ● term ● unit fraction ● whole number