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Structure: How are the four arithmetic operations related to each other?
Structure: How are the four arithmetic operations related to each other?
Multiplication and Division - How do the relationships between addition, subtraction, multiplication and division promote flexibility with numbers?
Multiplication and Division - How do the relationships between addition, subtraction, multiplication and division promote flexibility with numbers?
Students will use place value understanding to compose and decompose numbers, flexibly and fluently, in a variety of ways. Students will begin the year by exploring and operating with numbers larger than 10,000. They will gain the understanding that place values increase or decrease by multiples of 10. These skills will help them to apply this knowledge to perimeter problems and metric conversions.
Relationships between addition and multiplication as well as the relationships between subtraction and division lead to efficiency. Students will begin to explore and understand the concepts of multiples and factors of a number. Students will use multiple models, such as patterns, arrays, area models, partial products, partial quotients, etc. to develop concepts of multiplication and division including interpretation of remainders. These skills will help students solve problems involving area. They will then use this understanding to multiply and divide whole numbers in a variety of ways. Students will understand that relationships between the four operations facilitate flexibility with numbers and application with real world problems.
Common Core State Standards: 4.OA.1, 4.OA.2, 4.OA.3, 4.OA.4, 4.OA.5; 4.NBT.1, 4.NBT.2, 4.NBT.3, 4.NBT.4, 4.NBT.5, 4.NBT.6; 4.MD.1, 4.MD.3
Fractions and Decimals - How do fractions and decimals allow us to represent more precise values?
Fractions and Decimals - How do fractions and decimals allow us to represent more precise values?
Students will use fractions and decimals to represent more precise values and numbers. Using their knowledge of place value from unit one students will recognize that numbers can be composed and decomposed into parts of a whole using fractions and decimals. By understanding the relationship between the numerator and the denominator, students will be able to represent numbers in a variety of ways; for example number lines, equations, equivalencies, unit fractions, etc. These skills will help them to apply this knowledge to data and line plots and customary conversions and help students recognize how to apply them to real world problems.
Students’ previous knowledge of operations with whole numbers from Unit 1 will be applied to allow computation with fractions and decimals fluently and flexibly. Students will be able to add and subtract decimals and fractions with like denominators. They will also multiply a fraction by a whole number. Computation of fractions and decimals will be achieved through the use of number lines, estimation, rounding, and place value. Emphasis will be made to deepen students understanding of unit fractions so that they are able to compose and decompose fractions and solve more complex equations. Fractions and decimals allow us to represent and understand more precise values of numbers.
Common Core State Standards: 4.NF1, 4.NF.2, 4.NF.3 (a, b, c, d), 4.NF.4 (a, b, c), 4.NF.5, 4.NF.6, 4.NF.7; 4.MD.4
Geometry and Measurement – Why do mathematicians need precise language?
Geometry and Measurement – Why do mathematicians need precise language?
Students will identify and use attributes and properties of shapes and angles to classify 2 dimensional figures. Using appropriate tools, students will draw and measure 2 dimensional figures and angles. As students become familiar with angle measurement, they will explore and apply previous concepts of addition/subtraction to solve problems involving missing angle measurements as well as angle sums and differences. Students will not only be able to identify symmetrical figures, but also be able to draw the line(s) of symmetry in a given figure. Students will use knowledge of standard and metric systems for linear measurement, as well as volume and mass. Using this knowledge, students will convert units within a given system from larger to smaller units. Throughout the unit, students will apply concepts of geometry and measurement in real world problems. Through the use of multiple mathematical models students will understand that mathematicians communicate with precise geometric language to describe our world.
Common Core State Standards: 4.G.1, 4.G.2, 4.G.3, 4.MD.5 (a,b,), 4.MD.6, 4.MD.7, 4.MD.1, 4.MD.2, OA.5
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