Whole numbers 0-999
- Find equivalent representations for the same number
- Use models, explanations, or other representations to represent place value to the thousands place
- Order and compare numbers (ordinal and cardinal)
- Compare whole numbers to landmark numbers (e.g., 100, 250, 500, 1,000)
- Show the relationship between whole numbers
- Compose and decompose (e.g., 34 = 17+17; 34 = 29+5; 34 = 30+4)
- Connect number words and numerals to the quantities they represent
Fractional numbers
- Represent common fractions, such as halves, thirds, fourths, sixths, and eighths
- Represent a fraction as part of a whole (i.e., fraction of a set, fraction of an area)
- Compare or identify equivalent positive fractional numbers (e.g., a/2, a/3, a/4 where a is a whole number greater than 0 and less than or equal to the denominator)
- Use models, number lines, or explanations
Decimal numbers
- Represent decimals as part of 100 (within the context of money)
Operations
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- Use addition or subtraction of positive fractional numbers with like denominators
- Use addition or subtraction of decimals
- Describe or illustrate the inverse relationship between addition and subtraction or multiplication and division
- Describe the relationship between repeated addition and multiplication using models, number lines, or explanations
- accurately solves problems involving addition and subtraction using algorithm as one method with regrouping
Computation Fluency and Estimation
- Develop fluency in adding, subtracting, multiplying and dividing whole numbers
- Develop and use strategies to estimate the results of whole number computations
Patterns, Relationships, and Functions
- Identify specific cases of a variety of patterns both linear and non-numeric, represented in models, tables, words, graphs or sequences by extending the pattern to the next one, two, or three elements, or finding missing elements (geometric and numeric patterns
Algebraic Symbols
- Show the equality between two expressions using models or different representations of the expressions or by finding the value that will make an open sentence true (e.g., 2 + _ = 7) using one operation with addition, subtraction or multiplication
- solve mathematical problems to show relationships with equations
Mathematical Models
- Model problem situations with objects and use graphs, tables, equations to draw conclusions
Analysis of Change
- Introduce how a change in one variable relates to a change in a second variable
- Identify, describe, and/or compare situations that represent constant rates of change
Geometric Shapes
- Identify, compare, and analyze attributes or properties of angles (i.e., number of angles) or sides (i.e., number of sides or length of sides) of two and three-dimensional shapes
- Develop vocabulary to describe attributes and define classes of shapes such as triangles and pyramids
- Use composition or decomposition of shapes to identify, describe, or distinguish among triangles, squares, rectangles, rhombi, trapezoids, hexagons, or circles demonstrate congruence and similarity of shapes
Spatial Relationships
- Apply coordinate systems to specify locations and to describe paths
- Find location on a coordinate grid using positional words or compass directions interpret and give directions from one location to another using positional words
Transformations and Symmetry
- Predict and describe the results of sliding, flipping, and turning two-dimensional shapes
- Determine if two-plane figures are congruent by matching
- identify line (mirror) symmetry in two-dimensional models
Problem Solving
- Build, compare, copy, and draw geometric objects such as triangles, squares, rectangles, rhombi, trapezoids, hexagons, and circles
- Describe and create mental images of objects, patterns, and paths
- Identify and build models of rectangular prisms from three-dimensional representations
- Use geometric models to solve problems in other areas or disciplines
Units, Systems, and Processes of Measurement
- Compute perimeter of polygons
- Draw the area of rectangles on grids using a variety of models Express all measures using appropriate units
- Measure length, weight, and volume and select an appropriate type of unit for measuring
- Measure with standard units in the customary system
- Carry out simple unit conversions when solving problems across content strands use units of measures appropriately and consistent
Determining Measurement
- Estimate perimeters, area, and volumes of irregular shapes (benchmarks: quart to whole quart; kilogram to whole kilogram; gram to whole gram; pound to whole pound)
- Apply appropriate standard units and tools to measure length, area, volume, time, and temperature (benchmarks: hour to 5 minute interval; day; year; 24 hours in 1 day 7 days in 1 week; 365 days in 1 year; C degrees and F degrees to 1 degree)
- Use benchmarks to estimate measurements (benchmarks: inch to ½ inch; foot to whole inch; centimeter to whole centimeter; meter to whole centimeter)
- Use formulas to find the area of a rectangle
- analyze the parts of rectangular solids
Formulation of Questions
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- Interpret a given representation such as line plots, tally charts, tables, line graphs, or bar graphs to answer questions related to the data (Up and Down the Number Line, Inv. 2; Things That Come in Groups, Inv. 5)
- Collect data using observations, surveys and experiments
- Recognize the differences in representing categorical and numerical data
- formulate a question and develop a plan to collect information to address the question
- Answer questions related to the data
Analysis of Data
- Analyze patterns, trends or distributions in data in a variety of contexts by determining or using most frequent (mode), least frequent, largest, or smallest
- Identify or describe representations or elements of representations that best display a given set of data or situation using line plots, tally charts, tables or bar graphs
- Compare different representations of the same data and evaluate how well each representation shows important aspects of the data
Inferences and Predictions
- Make and justify predictions that are based on data
- analyze data to formulate conclusions or to make predictions
