Unit 2
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.
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.
Standards
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.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.
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.
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.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.
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.