Table of Contents
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Throughout Mathematics (Umbrella Concepts) FOCUS across all grades
Big Ideas 4th Grade
Numbers and Operations
- 4.1.2.1 Learn multiplication facts from 1-12 and corresponding division facts.
- 4.1.3.1 Represent equivalent fractions (halves to twelfths) using manipulatives including fraction circles, fraction strips, number lines and other manipulatives.
- 4.1.3.2 Using number lines and models to order and compare whole numbers, fractions (including improper and mixed numbers), and decimals (tenths).
- 4.1.3.4 Read and write tenths and hundredths in decimal and fraction notations using words and symbols.
- 4.1.3.8 Round to the nearest tenths.
- Common Vocabulary: Decimal, Equivalent, Factor, Denominator, Dividend, Improper Fraction, Mixed Number, Numerator, Operation, Quotient, Solve, Strategy,
- Notations: < less than, > greater than, (variables, boxes or blanks may be used for unknowns.
Algebra
Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems.
Input/Output tables
- 4.2.1.1 Input-Output Rules - Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table.
Number Sentences
- 4.2.2.2 Use number sentences involving multiplication, division and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.
Common Vocabulary: Solve
Geometry
4.3.1.1 & 4.3.1.2 Shapes
- Names of 2-D objects
- Ability to sketch a 2-D shape
- Describe and classify polygons using attributes such as how many angles and sides
- Address the question “what is a dimension?”
- a dimension is just a measurement. 2-D shapes have 2 measurements
4.3.2.1 &4.3.2.2 Angles
- Understand angle as measurable attributes of real-world and mathematical objects.
- Use various tools to measure angles.
- Understand and label acute, right, and obtuse angles
- The measurement of an angle is not dependent on the lengths of it’s sides, or the orientation of the angle
4.3.2.3 & 4.3.2.4 Area
- Understand area as measurable attributes of real-world and mathematical objects.
- Use various tools to measure area.
- Find the area of geometric shapes by counting how many (same-size) squares fit in a shape.
- Estimate the area in a non-geometric shape by counting how many (same-size) squares fit.
4,3,3,1- 4,3,3,4 Geometric Transformations
- No matter how a shape is moved, it maintains congruence
- Students can identify lines of symmetry, and draw figures with a line of symmetry.
Common Vocabulary: Acute Angle, Area, Clockwise, Counter Clockwise, Congruent, Horizontal, Image, Kite, Obtuse Angle, Parallelogram, Quadrilateral, Rectangle, Rhombus, Rotation, Square, Symmetry, Transformation, Translation, Trapezoid, Vertex, Vertical
Common Notation: 
or
Data Analysis and Probability
4.4.1.1 Collect & Interpret Data
- Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data.
(note: Use this throughout the year and incorporate into other subjects.)
Common Vocabulary: Venn Diagram, Survey, Timeline
Big Ideas 5th grade
Numbers and Operations
- 5.1.1.1 Multi-Digit Division Strategies - Divide multi-digit numbers, using procedures, based on knowledge of place value. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal.
- 5.1.1.2 Quotients in Context - Consider the context in which a problem is situated to select the most useful form of the quotient.
- 5.1.1.3 Estimation - Estimate solutions to arithmetic problems in order to assess the reasonableness of results.
- Students can use estimation skills in division and understand that not all quotients are whole numbers (e.g.
). - Students understand that remainders occur when numbers can’t divide evenly
- 5.1.2.1 Place Value - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions.
- 5.1.2.3 Number Line - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line.
- 5.1.2.4 Equivalent Fractions & Decimals - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts.
- 5.1.2.5 Round Decimals - Round numbers to the nearest 0.1, 0.01 and 0.001.
- Convert between fraction and decimal representations of a number including
.
Addition & Subtraction with Fractions
- 5.1.3.1 Addition & Subtraction Procedures - Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.
- 5.1.3.2 Representations - Model addition and subtraction of fractions and decimals using a variety of representations.
- 5.1.3.3 Estimation - Estimate sums and differences of decimals and fractions to assess the reasonableness of results.
- Add and subtract fractions with unlike denominators using manipulatives including fraction circles, fraction strips, and other manipulatives.
Common Vocabulary: Remainder
Common Notations: Fraction Bar
Algebra
- 5,2,1,1 Use tables and graphs to solve problems.
5.2.2.1 Properties and Expressions
- Generate equivalent numerical expressions using the order of operations
- Order of operations
- Parentheses
- Exponents
- Multiplication/Division (from left to right)
- Addition/Subtraction (from left to right)
5.2.3 Equations and Inequalities
- Understand what equalities and inequalities are.
- Equality - The condition of being equal in number or amount, being balanced =
- Inequality - The relation between two expressions that are not equal, employing a sign such as ≠ “not equal to,” > “greater than,” < “less than”
Common Vocabulary: Expression, Formula, Graph, Inequality, Line Graph, Ordered Pair,
Geometry
5.3.1.1 Three-Dimensional Figures
- Name, define, and classify 3-D shapes by the number of edges, faces, and vertices.
- Introduce depth as the third dimension.
- 5.3.1.2 Construct or Deconstruct a 3-D shape into a Net.
- 5.3.2.2 Through the use of manipulatives and eventually formulas students will be able to determine the volume and surface area and volume of rectangular prisms
Common Vocabulary: Base, Cone, Cube, Cylinder, Edge, Face, Height, Net, Prism, Pyramid, Surface Area, Three-Dimensional, Volume
Data Analysis and Probability
Mean, Median and Range, Bar and Line Graphs
- 5.4.1.1 Know how to find the mean, median and range of a data set.
- 5.4.1.2 Create and analyze double-bar graphs and line graphs.
Common Vocabulary: Double-Bar Graph, Maximum, Mean, Median, Minimum, Mode, Range,
Throughout Mathematics (Umbrella Concepts) FOCUS across all grades
- Teach vocabulary at content level and whenever possible expose them to vocabulary at grade level. (MCA III Vocab List)
- Embed mathematics into real world contexts and situations
If a student can show mastery of multiplication, division, and fraction concepts, by using manipulatives, but has difficulty performing the operations with standard algorithms then they may use a calculator to perform these tasks.