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UNIT 3 STANDARDS:
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
MGSE3.OA.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding
MGSE3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.2 For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Represent and interpret data.
MGSE3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
MGSE3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
Geometric Measurement: understand concepts of area and relate area to multiplication and to addition.
MGSE3.MD.5. Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
MGSE3.MD.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
MGSE3.MD.7. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show, in a concrete case, that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
OVERVIEW:
In this unit, students will:
●Understand concepts of area and relate area to multiplication and addition.
● Find the area of a rectangle with whole- number side lengths by tiling it.
● Multiply side lengths to find areas of rectangles with whole-number side lengths in context of solving real world and mathematical problems.
● Construct and analyze area models with the same product.
● Describe and extend numeric patterns. ● Determine addition and multiplication patterns.
● Understand the commutative property’s relationship to area.
● Create arrays and area models to find different ways to decompose a product.
● Use arrays and area models to develop understanding of the distributive property.
● Solve problems involving one and two steps and represent these problems using equations with letters such as “n” or “x” representing the unknown quantity.
● Create and interpret pictographs and bar graphs.
The understanding of and ability to use multiplication and division is the basis for all further mathematics work and its importance cannot be overemphasized. As students move through upper elementary grades and middle school, the foundation laid here will empower them to work with fractions, decimals, and percents.
Area is a measure of the space inside a region or how much it takes to cover a region. As with other attributes, students must first understand the attribute of area before measuring.
The concept of multiplication can be related to the area of rectangles using arrays. Students need to discover that the length of one dimension of a rectangle tells how many squares are in each row of an array and the length of the other dimension of the rectangle tells how many squares are in each column.
Using this model, students should be able to create arrays to solve real-life problems involving multiplication and apply this concept with addition, subtraction, and division to solve equations involving two steps or more to find the solution.
UNIT 3 STANDARDS:
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
MGSE3.OA.8. Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding
MGSE3.OA.9. Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations.2 For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed into two equal addends.
Represent and interpret data.
MGSE3.MD.3. Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs. For example, draw a bar graph in which each square in the bar graph might represent 5 pets.
MGSE3.MD.4. Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot, where the horizontal scale is marked off in appropriate units— whole numbers, halves, or quarters.
Geometric Measurement: understand concepts of area and relate area to multiplication and to addition.
MGSE3.MD.5. Recognize area as an attribute of plane figures and understand concepts of area measurement. a. A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area. b. A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.
MGSE3.MD.6. Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units).
MGSE3.MD.7. Relate area to the operations of multiplication and addition.
a. Find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths.
b. Multiply side lengths to find areas of rectangles with whole number side lengths in the context of solving real world and mathematical problems, and represent whole-number products as rectangular areas in mathematical reasoning.
c. Use tiling to show, in a concrete case, that the area of a rectangle with whole-number side lengths a and b + c is the sum of a × b and a × c. Use area models to represent the distributive property in mathematical reasoning.
OVERVIEW:
In this unit, students will:
●Understand concepts of area and relate area to multiplication and addition.
● Find the area of a rectangle with whole- number side lengths by tiling it.
● Multiply side lengths to find areas of rectangles with whole-number side lengths in context of solving real world and mathematical problems.
● Construct and analyze area models with the same product.
● Describe and extend numeric patterns. ● Determine addition and multiplication patterns.
● Understand the commutative property’s relationship to area.
● Create arrays and area models to find different ways to decompose a product.
● Use arrays and area models to develop understanding of the distributive property.
● Solve problems involving one and two steps and represent these problems using equations with letters such as “n” or “x” representing the unknown quantity.
● Create and interpret pictographs and bar graphs.
The understanding of and ability to use multiplication and division is the basis for all further mathematics work and its importance cannot be overemphasized. As students move through upper elementary grades and middle school, the foundation laid here will empower them to work with fractions, decimals, and percents.
Area is a measure of the space inside a region or how much it takes to cover a region. As with other attributes, students must first understand the attribute of area before measuring.
The concept of multiplication can be related to the area of rectangles using arrays. Students need to discover that the length of one dimension of a rectangle tells how many squares are in each row of an array and the length of the other dimension of the rectangle tells how many squares are in each column.
Using this model, students should be able to create arrays to solve real-life problems involving multiplication and apply this concept with addition, subtraction, and division to solve equations involving two steps or more to find the solution.