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- 3. Mathematical process standards
- 3.1. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- 3.1A. Apply mathematics to problems arising in everyday life, society, and the workplace.
- Let us add some numbers
- Let us subtract some numbers
- Place value subtraction
- Place value addition
- Word problems in division
- Make a Dollar from Cents
- Count the Cents and Exchange for Dollars
- Can you pay for the item?
- How many dollars and cents?
- Interpret a Bar Graph
- How much Pizza is remaining?
- Water the lawn
- Let us estimate the area of these shapes
- 3.1B. Use a problem-solving model that incorporates analyzing given information, formulating a plan or strategy, determining a solution, justifying the solution, and evaluating the problem-solving process and the reasonableness of the solution.
- 3.1C. Select tools, including real objects, manipulatives, paper and pencil, and technology as appropriate, and techniques, including mental math, estimation, and number sense as appropriate, to solve problems.
- Let us add some numbers
- Let us subtract some numbers
- Compare the two numbers
- Order the numbers
- Find the largest or smallest number
- Let us build a multiplication table
- Multiplication as repeated addition
- Multiplication fact family
- Divisibility Test for the number 3
- Divisibility Test for the number 6
- Divisibility Test for the number 9
- Compare Fractions using a Number Line
- Identify the right device
- Let us measure some lengths
- Measure using a ruler
- 3.1D. Communicate mathematical ideas, reasoning, and their implications using multiple representations, including symbols, diagrams, graphs, and language as appropriate.
- Compare the two numbers
- Order the numbers
- Find the largest or smallest number
- Identify the Place value of numbers
- Let us expand the number
- Write in expanded form
- Frame the division statement
- How many groups can you form?
- Divide using array model
- Interpret a Bar Graph
- Let us create a Bar Graph
- Find the hidden shapes
- Vertices and Sides. How many are there?
- Compare Fractions using a Number Line
- Vertices and sides in solid shapes
- Color the blocks
- Water the lawn
- What fraction is Colored?
- Write the fraction
- 3.1E. Create and use representations to organize, record, and communicate mathematical ideas.
- Let us identify the number
- Place value combinations
- Identify the Place value of numbers
- Let us expand the number
- Write in expanded form
- How many cents do I have?
- How many more cents do I need to pay to?
- Can you pay for the item?
- Give the correct change
- Can you represent using pictures?
- Let us build a Frequency Table
- Interpret a Bar Graph
- Let us create a Bar Graph
- Color the blocks
- Water the lawn
- What fraction is Colored?
- Write the fraction
- 3.1F. Analyze mathematical relationships to connect and communicate mathematical ideas.
- 3.1G. Display, explain, and justify mathematical ideas and arguments using precise mathematical language in written or oral communication.
- 3.1A. Apply mathematics to problems arising in everyday life, society, and the workplace.
- 3.1. The student uses mathematical processes to acquire and demonstrate mathematical understanding.
- 3. Number and operations
- 3.2. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value.
- 3.2A. Compose and decompose numbers up to 100,000 as a sum of so many ten thousands, so many thousands, so many hundreds, so many tens, and so many ones using objects, pictorial models, and numbers, including expanded notation as appropriate.
- 3.2B. Describe the mathematical relationships found in the base-10 place value system through the hundred thousands place.
- 3.2C. Represent a number on a number line as being between two consecutive multiples of 10; 100; 1,000; or 10,000 and use words to describe relative size of numbers in order to round whole numbers.
- 3.2D. Compare and order whole numbers up to 100,000 and represent comparisons using the symbols >, <, or =.
- 3.3. The student applies mathematical process standards to represent and explain fractional units.
- 3.3A. Represent fractions greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 using concrete objects and pictorial models, including strip diagrams and number lines.
- 3.3B. Determine the corresponding fraction greater than zero and less than or equal to one with denominators of 2, 3, 4, 6, and 8 given a specified point on a number line.
- 3.3C. Explain that the unit fraction 1/b represents the quantity formed by one part of a whole that has been partitioned into b equal parts where b is a non-zero whole number.
- 3.3D. Compose and decompose a fraction a/b with a numerator greater than zero and less than or equal to b as a sum of parts 1/b.
- 3.3E. Solve problems involving partitioning an object or a set of objects among two or more recipients using pictorial representations of fractions with denominators of 2, 3, 4, 6, and 8.
- 3.3F. Represent equivalent fractions with denominators of 2, 3, 4, 6, and 8 using a variety of objects and pictorial models, including number lines.
- 3.3G. Explain that two fractions are equivalent if and only if they are both represented by the same point on the number line or represent the same portion of a same size whole for an area model.
- 3.3H. Compare two fractions having the same numerator or denominator in problems by reasoning about their sizes and justifying the conclusion using symbols, words, objects, and pictorial models.
- 3.4. The student applies mathematical process standards to develop and use strategies and methods for whole number computations in order to solve problems with efficiency and accuracy.
- 3.4A. Solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
- Add cookies and packs of cookies
- Addition using Number Blocks
- Let us add some numbers
- Place value addition
- Fill the Addition Tree
- Can you Identify the Addition Pattern?
- Cookie Subtraction
- Subtraction using Number Blocks
- Let us subtract some numbers
- Fill the Subtraction Tree
- Can you Identify the Subtraction Pattern?
- Place value subtraction
- 3.4B. Round to the nearest 10 or 100 or use compatible numbers to estimate solutions to addition and subtraction problems.
- 3.4C. Determine the value of a collection of coins and bills.
- 3.4D. Determine the total number of objects when equally-sized groups of objects are combined or arranged in arrays up to 10 by 10.
- 3.4E. Represent multiplication facts by using a variety of approaches such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line, and skip counting.
- Introduction to Multiplication
- Let us add some objects
- Groups of objects
- Represent in groups and items
- Identify the correct picture
- Multiplication as repeated addition
- Represent the problem using strips
- Skip count using a number Line
- Let us do some skip counting
- Multiply using place value blocks
- Step by Step Multiplication
- 3.4F. Recall facts to multiply up to 10 by 10 with automaticity and recall the corresponding division facts.
- 3.4G. Use strategies and algorithms, including the standard algorithm, to multiply a two-digit number by a one-digit number. Strategies may include mental math, partial products, and the commutative, associative, and distributive properties.
- 3.4H. Determine the number of objects in each group when a set of objects is partitioned into equal shares or a set of objects is shared equally.
- 3.4I. Determine if a number is even or odd using divisibility rules.
- 3.4J. Determine a quotient using the relationship between multiplication and division.
- 3.4K. Solve one-step and two-step problems involving multiplication and division within 100 using strategies based on objects; pictorial models, including arrays, area models, and equal groups; properties of operations; or recall of facts.
- 3.4A. Solve with fluency one-step and two-step problems involving addition and subtraction within 1,000 using strategies based on place value, properties of operations, and the relationship between addition and subtraction.
- 3.2. The student applies mathematical process standards to represent and compare whole numbers and understand relationships related to place value.
- 3. Algebraic reasoning
- 3.5. The student applies mathematical process standards to analyze and create patterns and relationships.
- 3.5A. Represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations.
- Let us add some cookies
- Regrouping
- Add cookies and packs of cookies
- Addition using Number Blocks
- Add using Number Line
- Let us add some numbers
- Place value addition
- Fill the Addition Tree
- Can you Identify the Addition Pattern?
- Cookie Subtraction
- Subtraction using Number Blocks
- Subtract using Number Line
- Let us subtract some numbers
- Fill the Subtraction Tree
- Can you Identify the Subtraction Pattern?
- Place value subtraction
- 3.5B. Represent and solve one- and two-step multiplication and division problems within 100 using arrays, strip diagrams, and equations.
- 3.5C. Describe a multiplication expression as a comparison such as 3 x 24 represents 3 times as much as 24.
- 3.5D. Determine the unknown whole number in a multiplication or division equation relating three whole numbers when the unknown is either a missing factor or product.
- 3.5E. Represent real-world relationships using number pairs in a table and verbal descriptions.
- 3.5A. Represent one- and two-step problems involving addition and subtraction of whole numbers to 1,000 using pictorial models, number lines, and equations.
- 3.5. The student applies mathematical process standards to analyze and create patterns and relationships.
- 3. Geometry and measurement
- 3.6. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties.
- 3.6A. Classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language
- Properties of a Cube
- Properties of a Rectangular Prism
- Let us have a ball with Spheres
- Properties of a Cylinder
- Properties of a Cone
- Vertices and sides in solid shapes
- Let us play with rectangles
- Special form of rectangle called Square
- Let us create some rectangles
- Let us play with triangles
- Can you create some triangles?
- Let us play with circles
- Find the hidden shapes
- Vertices and Sides. How many are there?
- Triangular Prisms
- Properties of a Parallelogram
- Special form of Parallelogram - Rhombus
- Properties of a Trapezium
- Identify these shapes
- Identify shapes by the number of sides
- 3.6B. Use attributes to recognize rhombuses, parallelograms, trapezoids, rectangles, and squares as examples of quadrilaterals and draw examples of quadrilaterals that do not belong to any of these subcategories.
- 3.6C. Determine the area of rectangles with whole number side lengths in problems using multiplication related to the number of rows times the number of unit squares in each row.
- 3.6D. Decompose composite figures formed by rectangles into non-overlapping rectangles to determine the area of the original figure using the additive property of area.
- 3.6E. Decompose two congruent two-dimensional figures into parts with equal areas and express the area of each part as a unit fraction of the whole and recognize that equal shares of identical wholes need not have the same shape.
- 3.6A. Classify and sort two- and three-dimensional figures, including cones, cylinders, spheres, triangular and rectangular prisms, and cubes, based on attributes using formal geometric language
- 3.7. The student applies mathematical process standards to select appropriate units, strategies, and tools to solve problems involving customary and metric measurement.
- 3.7A. Represent fractions of halves, fourths, and eighths as distances from zero on a number line.
- 3.7B. Determine the perimeter of a polygon or a missing length when given perimeter and remaining side lengths in problems.
- 3.7C. Determine the solutions to problems involving addition and subtraction of time intervals in minutes using pictorial models or tools such as a 15-minute event plus a 30-minute event equals 45 minutes.
- 3.7D. Determine when it is appropriate to use measurements of liquid volume (capacity) or weight.
- 3.7E. Determine liquid volume (capacity) or weight using appropriate units and tools.
- 3.6. The student applies mathematical process standards to analyze attributes of two-dimensional geometric figures to develop generalizations about their properties.
- 3. Data analysis
- 3.8. The student applies mathematical process standards to solve problems by collecting, organizing, displaying, and interpreting data.
- 3. Personal financial literacy
- 3.9. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security.
- 3.9A. Explain the connection between human capital/labor and income.
- 3.9B. Describe the relationship between the availability or scarcity of resources and how that impacts cost.
- 3.9C. Identify the costs and benefits of planned and unplanned spending decisions.
- 3.9D. Explain that credit is used when wants or needs exceed the ability to pay and that it is the borrower's responsibility to pay it back to the lender, usually with interest.
- 3.9E. List reasons to save and explain the benefit of a savings plan, including for college.
- 3.9F. Identify decisions involving income, spending, saving, credit, and charitable giving.
- 3.9A. Explain the connection between human capital/labor and income.
- 3.9. The student applies mathematical process standards to manage one's financial resources effectively for lifetime financial security.