Whole Numbers
Introduction to Whole Numbers
Students are introduced to whole numbers and the place value chart. They sort number, identify the value of digits in different places, and practice rounding.
2.NBT.A.1
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Adding Whole Numbers
Students learn vocabulary terms that can be used to represent addition. They use place value to add whole numbers with the traditional algorithm. They practice adding multi-digit numbers.
2.OA.A.1
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Subtracting Whole Numbers
Students learn vocabulary terms that can be used to represent subtraction. They use place value to subtract whole numbers with the traditional algorithm. They practice subtracting multi-digit numbers.
2.OA.A.1
Multiplying Whole Numbers
Students learn vocabulary terms that can be used to represent multiplication. They use place value to multiply whole numbers with the traditional algorithm. They practice multiplying multi-digit numbers.
3.OA.A.1
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Dividing Whole Numbers
Students learn vocabulary terms that can be used to represent division. They use place value to divide whole numbers with the traditional algorithm (long division). They practice dividing multi-digit numbers.
3.OA.A.2
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Problem-Solving with Whole Numbers
Students solve word problems, identifying which operations to use and calculating
accurately. 3.OA.D.8
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Fraction
Concepts From Whole Numbers to Rational Numbers
Students watch an animation describing how whole numbers are represented as fractions and what each part of the fraction means.
Students use whole numbers as fractions to see that adding or subtracting across with fractions gives incorrect sums and differences.
Throughout the rest of the workspace, students write two fractions to represent models.
3.NF.3c
1 The Real and Complex Number System
Animations Classifications Explore Tools Graphing Tools Interactive Diagrams Interactive Worksheets Proof Real-World Scenarios Solvers Worked Example
MATHia Unit MATHia Workspace Overview CCSS Concept
Builder Mastery
Fraction Concepts (continued)
Models of Fractions
Students build area, set, and number line models of given fractions by describing the meaning of the denominator and then the numerator. Students then compare the fraction and its model to 1 whole.
3.NF.1 3.NF.2
Benchmark Fractions
Students watch an animation showing fractions close to 1, close to 1 half, and close to 0 in real-world contexts. Students learn ways to decide whether a fraction is close to 0 or close to 1 and then use this knowledge to compare fractions. Students then learn ways to decide whether a fraction is less than 1, equal to 1, or greater than 1. They use this knowledge to compare fractions.
Students then sort fractions by estimating.
Finally, students explore estimating fractions by playing an estimation game on a blank number line.
3.NF.3d
Representing Groups as Fractions
Representing Parts of Groups using Fractions
Students use concrete part-to-whole models to represent a fraction and an equivalent fraction, calculating the numerator of the fraction with the larger denominator.
4.NF.A.1
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Representing Group Totals using Fractions
Students use concrete part-to-whole models to represent a fraction and an equivalent fraction, calculating the denominator of the fraction with the larger denominator.
4.NF.A.1
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Representing Parts of Groups or Group Totals using Fractions
Students use abstract part-to-whole models to represent a fraction and an equivalent fraction, calculating the numerator or the denominator of the fraction with the larger denominator.
4.NF.A.1
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Equivalent Fractions
Writing Equivalent Fractions using Part-to-Whole Models
Students use part-to-whole models to determine fractions with given denominators that are equivalent to given simplified fractions.
3.NF.A.3
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Writing Simplified Fractions using Part-to-Whole Models
Students use part-to-whole models to determine simplified forms of given
equivalent fractions. 3.NF.A.3.b
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Equivalent Fractions (continued)
Comparing Fractions using Symbols
Students compare pairs of fractions in context, both symbolically and contextually,
first converting them to LCD form if needed. 4.NF.A.2
Multiplying by Fractions to Increase or Decrease Quantities
Students watch an animation showing how multiplying by a fraction can increase a quantity, decrease a quantity, or keep a quantity the same. Students reason with fractional factors that are less than 1, equal to 1, or greater than 1 to determine how they affect the resulting product.
5.NF.B.5.a
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Fraction Addition and Subtraction
Using Models with Like Denominator Fractions
Students use number line and fraction strips models to add and subtract fractions with like denominators. They use fraction strips models for operating with proper fractions (those less than 1) and number line models for operating with both proper and improper fractions-- fractions that are equal to or greater than 1. In this workspace, students do not rewrite sums and differences in lowest terms.
4.NF.3a
Using Models with Unlike Denominator Fractions
Students use number line and fraction strips models to add and subtract fractions with unlike denominators. They use fraction strips models for operating with proper fractions (those less than 1) and number line models for operating with proper fractions, improper fractions, and mixed numbers.
5.NF.1
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Using the Solver with Unlike
Denominator Fractions Students calculate sums and differences of
proper fractions with unlike denominators. 5.NF.1
Mixed Number Addition and Subtraction
Adding and Subtracting with Like Denominators
Students calculate sums and differences of mixed numbers and improper fractions with
like denominators. 4.NF.B.3
Adding and Subtracting with Unlike Denominators
Students calculate sums and differences of mixed numbers and improper fractions with
unlike denominators. 5.NF.A.1
Decimals and
Place Value Writing Money Amounts using Place Value
Students use their knowledge of money to select the place value and digits of a given amount. The given amount can be stated as a number or in words.
5.NBT.A.3
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1 The Real and Complex Number System
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MATHia Unit MATHia Workspace Overview CCSS Concept
Builder Mastery
Decimals and Place Value (continued)
Writing Decimals using Place Value
Students select the place value and digit of a given value that is written to three significant digits. The given amount can be stated as a number or in words.
5.NBT.A.3
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Identifying Place Values and Digits of Decimals
Students select the place value of a given digit, which is embedded in a number that is written to the thousands and thousandths place value. The student must also enter the digit that appears in a given place value.
5.NBT.A.3
Fraction and Decimal Conversions
Converting Decimals to
Fractions Students write fractional equivalents of
decimal values. 4.NF.C.6
Converting Decimal Fractions to Decimals
Students write decimal equivalents of fractional values with power of ten
denominators. 4.NF.C.6
Picture Algebra
Using Picture Algebra with Multiplication
Students use pictures to represent problems that involve a larger quantity, a smaller quantity, and a total. The relationship between the two quantities involves multiplication.
3.OA.A.3
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Using Picture Algebra with Addition
Students use pictures to represent problems that involve a larger quantity, a smaller quantity, and a total. The relationship between the two quantities involves addition.
2.OA.A.1
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Using Picture Algebra with Subtraction
Students use pictures to represent problems that involve a larger quantity, a smaller quantity, and a total. The relationship between the two quantities involves subtraction.
2.OA.A.1
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Expression Evaluation using Whole Numbers
Evaluating One-Step Expressions with Whole Numbers
Students determine relevant information from scenarios and use this information to evaluate
algebraic expressions with a single operation. 6.EE.A.2
Evaluating Two-Step Expressions with Whole Numbers
Students determine relevant information from scenarios and use this information to evaluate
algebraic expressions with two operations. 6.EE.A.2
Solving One-Step Equations with Decimals
Solving One-Step Equations with Decimals (No Type In)
Students use an equation solver and inverse operations to solve a variety of one-step equations involving decimal coefficients and constants.
Solving One-Step Equations with Decimals (Type In)
Students use an equation solver and inverse operations to solve a variety of one-step equations involving decimal coefficients and constants.
Solving One-Step Equations with Fractions
Solving One-Step Equations with Fractions (No Type In)
Students use an equation solver and inverse operations to solve a variety of one-step equations involving fractional coefficients and constants.
Solving One-Step Equations with Fractions (Type In)
Students use an equation solver and inverse operations to solve a variety of one-step equations involving fractional coefficients and constants.
2 Operations & Algebraic Thinking
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MATHia Unit MATHia Workspace Overview CCSS Concept
Builder Mastery Solving Two-Step
Equations with Decimals
Solving Two-Step Equations
with Decimals (No Type In) Students solve two-step equations involving
decimal coefficients and constants.
Solving Two-Step Equations
with Decimals (Type In) Students solve two-step equations involving
decimal coefficients and constants.
Solving Two-Step Equations with Fractions
Solving Two-Step Equations
with Fractions (No Type In) Students solve two-step equations involving
fractional coefficients and constants.
Solving Two-Step Equations
with Fractions (Type In) Students solve two-step equations involving
fractional coefficients and constants.
Angles and Angle Pairs
Measuring Angles
Students use a protractor to measure acute, right, obtuse and straight angles. Students use both the inside and outside scales of a protractor to measure angles. The angles presented are given in a variety of different orientations.
4.MD.C.5
4.MD.C.6
Classifying Angles
Students sort and classify acute, right, obtuse, and straight angles as well as angles that do not match any of these categories. Sorting is done using numerical angle measures as well as depictions of angles.
4.MD.C.5
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Triangles, Quadrilaterals, and Other Polygons
Classifying Triangles
Students sort and classify triangles according to their measures and according to their side lengths. Students sort acute, right, and obtuse triangles as well as isosceles, equilateral, and scalene triangles.
5.NBT.A.3
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Classifying Quadrilaterals
Students sort and classify quadrilaterals (parallelograms, rectangles, rhombuses, squares, and trapezoids) given their properties, including side lengths and angle measures. Students choose the best description for quadrilaterals that can be assigned to two or more categories.
5.NBT.A.3
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Classifying Polygons Students sort and classify regular and irregular polygons given information about
their side lengths and angle measures. 4.G.A.2
