Unit 1 - Creating Classroom community through
DATA & GRAPHING
Standards
5.G.1 Understand how to graph ordered pairs on a coordinate plane.
5.G.2 Graph and interpret points in the first quadrant of a coordinate plane.
5.OA.3 Generate two numerical patterns using two given rules.
5.G.1 Understand how to graph ordered pairs on a coordinate plane.
5.G.2 Graph and interpret points in the first quadrant of a coordinate plane.
5.OA.3 Generate two numerical patterns using two given rules.
Students will understand that:
- x and y coordinates can be interpreted to solve problems. (NC.5.G.1)
- Different questions yield different types of data - categorical or numerical. (NC.5.MD.2)
- Line graphs can be used to represent data that changes over time. (NC.5.MD.2)
- Line graphs can be used to show how shape patterns grow. (NC.5.MD.2)
- Numerical patterns can be generated using rules. (NC.5.OA.3)
UNIT 1 - SUMMARY
Students will be able to:
Determine whether data is categorical data or numerical
Categorical data represent characteristics such as a person's gender, hometown, or the types of movies they like.
Numerical data is data that is measurable, such as time, height, weight, amount, and so on.
Determine whether data is categorical data or numerical
Categorical data represent characteristics such as a person's gender, hometown, or the types of movies they like.
Numerical data is data that is measurable, such as time, height, weight, amount, and so on.
- Ask questions that will yield data that changes over time, collect the data, represent it using a line graph, and answer questions about the data.
- Generate two numerical patterns using two given rules
- Form ordered pairs using corresponding terms in two numerical patterns
- Generate ordered pairs that show how a shape pattern grows from term to term
- Identify and interpret x and y coordinates
- Graph x and y points in the first quadrant of a coordinate plane to solve problems
UNIT 1 - VOCABULARY
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Unit 2 - Part 1
VOLUME -
using models to explore properties of multiplication and division
Standards
5. MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
5. MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
5. MD.3 Recognize volume as an attribute of solid figures and understand concepts of volume measurement.
- A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume.
- A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.
5. MD.5 Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume.
Students will understand that:
- There is a set order of operations to use when solving problems. (NC.5.OA.2)
- Strategies based on distributive, associative, and commutative properties can be used to multiply and divide whole numbers. (NC.5.OA.2)
- Volume is an attribute of solid figures. (NC.5.MD.4)
- There is a connection between volume found by packing with unit cubes and the volume found by multiplying whole-number edge lengths. (NC.5.MD.5)
- The volume of a solid figure composed of two non-overlapping rectangular prisms is the same as the sum of the volume of the two separate rectangular prisms. (NC.5.MD.5)
Vocabulary
Cubic Units: unit used to measure the volume of a solid
Dimension: a measure of length in one direction
Rectangular Prism: a three-dimensional figure with six rectangular faces
Volume: the measurement of the amount of space taken up by something with three dimensions
Cubic Units: unit used to measure the volume of a solid
Dimension: a measure of length in one direction
Rectangular Prism: a three-dimensional figure with six rectangular faces
Volume: the measurement of the amount of space taken up by something with three dimensions
Questions to Consider:
- Explain how to find the volume of a rectangular prism without using a formula.
- Explain why the formula for volume- V = l x w x h is used to find volume.
- Explain why the formula V = b x h is used to find volume. How does this relate to finding area?
- Explain the difference between using V = l x w x h and V = b x h. Describe why both of these formulas work when finding volume.
- Explain why knowing your multiplication facts are beneficial when you are asked to find the missing measurements when given the volume of a figure.
- Describe how you determine how to decompose composite figures in order to find volume.
Finding Volume of Composite Prisms |
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unit 2 - Part 2
multiplying whole numbers - 5.nbt.5
fluently mutiply multi-digit whole numbers using models
Multiplication Strategies
Rectangle Sections Model (Area Model) The Rectangle Sections method helps organize the parts of a multi-digit multiplication problem. Decompose each factor and multiply to find partial products. Add the partial products to find the answer to the multiplication problem Standard Algorithm Students must gain fluency with the standard algorithm in fifth grade. Remember to think about why you are doing what you are doing as you complete the various steps. How did you get 1,516 as your first partial product? Why do we need the placeholder "0"? |
Unit 2 - Part 3
dividing WHOLE NUMBERS - 5.NBT.6
Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.
Division Strategies
Area Model
An area model for division is shown here. As you use the area model, keep track of how much of the 2464 is left to divide. Make sure you are dividing with reasonable numbers (consider powers of ten and use benchmark numbers to help). Expanded Notation (aka Stacking Method & similar to Partial Quotients) The expanded notation strategy for division also allows students to use reasonable numbers (benchmark numbers, powers of ten) to divide. Please take a moment to watch these videos to provide examples of this strategy. |
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