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.
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:
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
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 =.
• 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 =.