Unit 1 - Number puzzles and multiple towers
In the first of two units about multiplication and division, students continue to develop and practice efficient strategies to solve multiplication problems both in and out of a context. Students refine and gain fluency in solving two-digit by two-digit multiplication problems, develop strategies for division problems with one- and two-digit divisors, and increase their knowledge of multiplication relationships by learning about prime factorization (e.g., 36 = 4 x 9 = (2 x 2) x 9 = 2 x 2 x 3 x 3)
Lesson Essential Questions:
What is the relationship between a number and its multiples and factors.?
What are the characteristics of a number?
How do factors allow us to find products?
How do we write and interpret numerical expressions?
What is the relationship between multiplication and division?
How do division strategies allow us to find quotients?
Vocabulary:
factors, prime, square, array, prime factorization, factor pairs, composite, dimensions, multiple, multiplication, dividend, divisor, quotient, remainder, division, product, equivalent, doubling, halving, order of operations
Lesson Essential Questions:
What is the relationship between a number and its multiples and factors.?
What are the characteristics of a number?
How do factors allow us to find products?
How do we write and interpret numerical expressions?
What is the relationship between multiplication and division?
How do division strategies allow us to find quotients?
Vocabulary:
factors, prime, square, array, prime factorization, factor pairs, composite, dimensions, multiple, multiplication, dividend, divisor, quotient, remainder, division, product, equivalent, doubling, halving, order of operations
unit 2 - prisms & pyramids
Students investigate concepts of volume by finding the volume of prisms, pyramids, cylinders, and cones. They use patterns of open boxes and build prisms from cubes to develop a strategy for finding the volume of any rectangular prism. Using concrete materials, they also examine the 3-to-1 volume relationship between related (having the same base and height) prisms and pyramids, and related cylinders and cones. Geometry work includes naming geometric solids and their attributes.
Lesson Essential Questions:
How do we manipulate 2D figures to create 3D figures?
What strategies can be used to find the volume of rectangular prisms?
How do we find the volume of a solid composed of two rectangular prisms?
How does changing dimensions of a rectangular prism impact its volume?
Vocabulary:
attributes, volume, dimensions, length, width, height, cube, rectangular prism, 3D, base, cubic units
Lesson Essential Questions:
How do we manipulate 2D figures to create 3D figures?
What strategies can be used to find the volume of rectangular prisms?
How do we find the volume of a solid composed of two rectangular prisms?
How does changing dimensions of a rectangular prism impact its volume?
Vocabulary:
attributes, volume, dimensions, length, width, height, cube, rectangular prism, 3D, base, cubic units
unit 3 - thousands of miles, thousands of seats
Students study place value in large numbers by building a 10,000 chart and by adding multiples of 10 to and subtracting multiples of 10 from four- and five- digit numbers. Students finalize their study of subtraction by refining and gaining fluency in solving subtraction problems, including a study of the U.S. algorithm for subtraction. Using a context of the capacities of stadiums and arenas, they solve addition and subtraction problems involving four- and five- digit numbers. Students also demonstrate fluency with the division facts up to 144 ÷ 12.
Lesson Essential Questions:
How do we use landmark numbers such as tens, hundreds, thousands, and
ten-thousands to help us add and subtract?
How can we represent numbers in different ways to show place value?
How does your understanding of place value help us to add and subtract efficiently?
How do we interpret and solve real world problems?
Vocabulary:
standard form, expanded form, written form, exponential form, place value, representation, operation, algorithm, addition, subtraction, inverse relationship, interpret
Lesson Essential Questions:
How do we use landmark numbers such as tens, hundreds, thousands, and
ten-thousands to help us add and subtract?
How can we represent numbers in different ways to show place value?
How does your understanding of place value help us to add and subtract efficiently?
How do we interpret and solve real world problems?
Vocabulary:
standard form, expanded form, written form, exponential form, place value, representation, operation, algorithm, addition, subtraction, inverse relationship, interpret