Growing with Mathematics

Grade Four

Growing With Mathematics

GWM Content/
Lessons /

State

Indicators

Lessons/Indicators: / Timeline / Assessment / Comments
Exploring Math
Exploring Math (cont.) / 1.1/1.3- G2 Describe, classify, compare and model two- and three-dimensional objects using their attributes.
1.1/1.2/1.3/1.4/1.5 - M5 Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons.
1.1/1.2/1.5 - NSO 2 Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.
1.1 - NSO 11 Develop and explain strategies for performing computations mentally.
1.3 - G3 Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids.
1.3 - G4 Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles).
1.3 - NSO 9 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
1.3/1.5 - NSO 14Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
1.4 - NSO 8 Solve problems involving counting money and making change, using both coins and paper bills.
1.4 - NSO 12 Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.
1.4 - G 1 Identify, describe and model intersecting, parallel and perpendicular lines and line segments; e.g., use straws or other material to model lines.
1.5 - DAP 2 Represent and interpret data using tables, bar graphs, line plots and line graphs.
1.5 - DAP 5 Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs.
1.5 - NSO 1a Identify and generate equivalent forms of fractions and decimals. For example:
a.Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., , , “five tenths,” 0.5, shaded rectangles with half, and five tenths. / September
September / Assessment: pp. 12-16
1.4 Add vocabulary: intersecting, perpendicular
Assessment: pp. 12-16
1.4 Add vocabulary: intersecting, perpendicular
Investigating Length
Investigating Length (cont.)
Investigating Length (cont.) / 2.1/2.4 – NSO 9 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
2.1/2.2/2.4 - NSO 11 Develop and explain strategies for performing computations mentally.
2.1/2.2 - NSO 12 Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.
2.1/2.2/2.4 - NSO 14Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
2.1 - M 4 Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume.
2.1/2.3/2.5 - M 6 Write, solve and verify solutions to multi-step problems involving measurement.
2.1 - G4 Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles).
2.2/2.3/2.5 – NSO 2 Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.
2.2/2.3/2.4/2.5 - M 5 Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons.
2.2 - DAP 2 Represent and interpret data using tables, bar graphs, line plots and line graphs.
2.2 - DAP 5 Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs.
2.3/2.4 – M 1 Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher.
2.3 - PFA 1 Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications.
2.3 - G2 Describe, classify, compare and model two- and three-dimensional objects using their attributes.
2.4 - NSO 13Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.
MD 1: Know relative sizes of measurement units within one system of units including km, m, cm; kg, g; lb, oz.; l, ml; hr, min, sec. Within a single system of measurement, express measurements in a larger unit in terms of a smaller unit. Record measurement equivalents in a two-column table. For example, know that 1 ft is 12 times as long as 1 in. Express the length of a 4 ft snake as 48 in. Generate a conversion table for feet and inches listing the number pairs (1, 12), (2, 24), (3, 36), ...
MD 2: Use the four operations to solve word problems involving distances, intervals of time, liquid volumes, masses of objects, and money, including problems involving simple fractions or decimals, and problems that require expressing measurements given in a larger unit in terms of a smaller unit. Represent measurement quantities using diagrams such as number line diagrams that feature a measurement scale. / September
September
September / Assessment: pp. 18-22
Assessment: pp. 18-22
Assessment: pp. 18-22
Using Addition and Subtraction
Using Addition and Subtraction (cont.) / 3.1 – NSO 2 Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.
3.1 - NSO 4 Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite.
3.1 - NSO 7 Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.
3.1/3.2/3.3/3.4/3.5 - NSO 11 Develop and explain strategies for performing computations mentally.
3.1/3.2/3.3/3.4/3.5 - NSO 12 Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.
3.1/3.2/3.3/3.4/3.5 - NSO 14Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
3.1/3.3/3.4 - PFA 1 Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications.
3.1 - PFA 2 Represent and analyze patterns and functions using words, tables and graphs.
3.2/3.3/3.4/3.5 – NSO 5 Use models and points of reference to compare commonly used fractions.
3.2 - PFA 5 Represent mathematical relationships with equations or inequalities.
3.2 - DAP 5 Propose and explain interpretations and predictions based on data displayed in tables, charts and graphs.
3.3/3.4/3.5 - NSO 8 Solve problems involving counting money and making change, using both coins and paper bills.
3.3/3.4/3.5 - NSO 9 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
3.3 - NSO 10 Use physical models, visual representations, and paper and pencil to add and subtract decimals and commonly used fractions with like denominators.
3.5 - DAP 2 Represent and interpret data using tables, bar graphs, line plots and line graphs.
NOBT 4: Fluently add and subtract multi-digit whole numbers using the standard algorithm. / September
September
September / Assessment: pp. 24-28
Assessment: pp. 24-28
Assessment: pp. 24-28
Investigating 5-Digit Numbers
Investigating 5-Digit Numbers (cont.)
Investigating 5-Digit Numbers (cont.) / 4.1/4.2/4.3/4.4/4.5 – NSO 2 Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.
4.1 - NSO 7 Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.
4.1/4.2/4.3/4.4/4.5 - NSO 11 Develop and explain strategies for performing computations mentally.
4.1/4.2/4.3/4.4/4.5 - NSO 12 Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.
4.1 - M 4 Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume.
4.1 - M 6 Write, solve and verify solutions to multi-step problems involving measurement.
4.2 - NSO 9 Estimate the results of computations involving whole numbers, fractions and decimals, using a variety of strategies.
4.2/4.3/4.4/4.5 - NSO 13Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.
4.2/4.4/4.5 - NSO 14Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
4.2 - M 1 Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher.
4.2 - M 5 Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons.
4.3/4.5 - DAP 2 Represent and interpret data using tables, bar graphs, line plots and line graphs.
4.3 - PFA 1 Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications.
4.3/4.5 - PFA 2 Represent and analyze patterns and functions using words, tables and graphs.
4.4/4.5 - NSO 5 Use models and points of reference to compare commonly used fractions.
4.5 - G2 Describe, classify, compare and model two- and three-dimensional objects using their attributes.
NOBT 1: Recognize that in a multi-digit whole number, a digit in one place represents ten times what it represents in the place to its right. For example, recognize that 700 ÷ 70 = 10 by applying concepts of place value and division.
NOBT 2: Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons. / October
October / Assessment: pp. 30-34
Assessment: pp. 30-34
Investigating Shapes and Angles
Investigating Shapes and Angles (cont.)
Investigating Shapes and Angles (cont.) / 5.1 – G Benchmark H, NSO 2 Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.
5.1/5.2/5.3/5.5 – NSO 6 Use associative and distributive properties to simplify and perform computations; e.g., use left to right multiplication and the distributive property to find an exact answer without paper and pencil, such as 5 x 47 = 5 x 40 + 5 x 7 = 200 + 35 = 235.
5.1/5.2/5.4/5.5 – NSO 14Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
5.1/5.3 – G 7 Identify, describe and use reflections (flips), rotations (turns), and translations (slides) in solving geometric problems; e.g., use transformations to determine if 2 shapes are congruent.
5.1/5.2/5.3/5.5 – PFA 6 Describe how a change in one variable affects the value of a related variable; e.g., as one increases the other increases or as one increases the other decreases.
5.2 – G Benchmark H
5.3 – NSO 1 Identify and generate equivalent forms of fractions and decimals. For example:
a.Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., , , “five tenths,” 0.5, shaded rectangles with half, and five tenths.
b.Understand and explain that ten tenths is the same as one whole in both fraction and decimal form.
5.3 – NSO 5 Use models and points of reference to compare commonly used fractions.
5.3/5.5 – G8 Benchmark D Use geometric models to solve problems in other areas of mathematics, such as number (multiplication/division) and measurement (area, perimeter, border).
5.4 – NSO 11 Develop and explain strategies for performing computations mentally.
5.4 – NSO 13Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.
5.4/5.5 – G2 Describe, classify, compare and model two- and three-dimensional objects using their attributes.
5.4/5.5 – G3 Identify similarities and differences of quadrilaterals; e.g., squares, rectangles, parallelograms and trapezoids.
5.4/5.5 – G4 Identify and define triangles based on angle measures (equiangular, right, acute and obtuse triangles) and side lengths (isosceles, equilateral and scalene triangles).
5.5 – NSO 12 Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.
G 1: Draw points, lines, line segments, rays, angles (right, acute, obtuse), and perpendicular and parallel lines. Identify these in two-dimensional figures.
G 3: Recognize a line of symmetry for a two-dimensional figure as a line across the figure such that the figure can be folded along the line into matching parts. Identify line-symmetric figures and draw lines of symmetry. / October
October / Assessment: pp. 36-40
Assessment: pp. 36-40
Finding Fractions
Finding Fractions (cont.)
Finding Fractions (cont.)
Finding Fractions (cont.) / 6.1/6.2/6.3/6.4/6.5 – NSO 2 Use place value structure of the base-ten number system to read, write, represent and compare whole numbers through millions and decimals through thousandths.
6.1/6.2/6.3/6.4/6.5 – NSO 5 Use models and points of reference to compare commonly used fractions.
6.1/6.2/6.3/6.4/6.5 – NSO 7 Recognize that division may be used to solve different types of problem situations and interpret the meaning of remainders; e.g., situations involving measurement, money.
6.1/6.2/6.3/6.4/6.5 – NSO 11 Develop and explain strategies for performing computations mentally.
6.1/6.2/6.3/6.4/6.5 – NSO 12 Analyze and solve multi-step problems involving addition, subtraction, multiplication and division using an organized approach, and verify and interpret results with respect to the original problem.
6.1/6.2 – NSO 13 Use a variety of methods and appropriate tools for computing with whole numbers; e.g., mental math, paper and pencil, and calculator.
6.1/6.4/6.5 – NSO 14 Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
6.1 – M1 Relate the number of units to the size of the units used to measure an object; e.g., compare the number of cups to fill a pitcher to the number of quarts to fill the same pitcher.
6.1/6.3 – M2 Demonstrate and describe perimeter as surrounding and area as covering a two-dimensional shape, and volume as filling a three-dimensional object.
6.1 – M3aIdentify and select appropriate units to measure:
a.perimeter – string or links (inches or centimeters).
6.1/6.2/6.3/6.4/6.5 – PFA 1 Use models and words to describe, extend and make generalizations of patterns and relationships occurring in computation, numerical patterns, geometry, graphs and other applications.
6.1/6.2/6.4/6.5 – PFA 2 Represent and analyze patterns and functions using words, tables and graphs.
6.3 – M4 Develop and use strategies to find perimeter using string or links, area using tiles or a grid, and volume using cubes; e.g., count squares to find area of regular or irregular shapes on a grid, layer cubes in a box to find its volume.
6.3 – NSO 14 M Benchmark C - Demonstrate fluency in adding and subtracting whole numbers and in multiplying and dividing whole numbers by 1- and 2-digit numbers and multiples of ten.
6.4/6.5 – NSO 1a Identify and generate equivalent forms of fractions and decimals. For example:
a.Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., , , “five tenths,” 0.5, shaded rectangles with half, and five tenths.
6.4/6.5 – G8 Use geometric models to solve problems in other areas of mathematics, such as number (multiplication/division) and measurement (area, perimeter, border).
6.5 – NSO 4 Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite.
6.5 – M5 Make simple unit conversions within a measurement system; e.g., inches to feet, kilograms to grams, quarts to gallons.
6.5 - M Benchmark C
NSF 1: Explain why a fraction a/b is equivalent to a fraction (n × a)/(n × b) by using visual fraction models, with attention to how the number and size of the parts differ even though the two fractions themselves are the same size. Use this principle to recognize and generate equivalent fractions.
NSF 2: Compare two fractions with different numerators and different denominators, e.g., by creating common denominators or numerators, or by comparing to a benchmark fraction such as 1/2. Recognize that comparisons are valid only when the two fractions refer to the same whole. Record the results of comparisons with symbols >, =, or <, and justify the conclusions, e.g., by using a visual fraction model. / October
October
October / Assessment: pp. 42-46
Assessment Topics 1-6, pp. 47-50
Assessment: pp. 42-46
Assessment Topics 1-6, pp. 47-50
Assessment: pp. 42-46
Assessment Topics 1-6, pp. 47-50
Multiplying by 1-Digit Numbers
Multiplying by 1-Digit Numbers (cont.)
Multiplying by 1-Digit Numbers (cont.) / 7.1/7.4 – NSO 1 Identify and generate equivalent forms of fractions and decimals. For example:
a.Connect physical, verbal and symbolic representations of fractions, decimals and whole numbers; e.g., , , “five tenths,” 0.5, shaded rectangles with half, and five tenths.
b.Understand and explain that ten tenths is the same as one whole in both fraction and decimal form.
7.1/7.2 – NSO 4 Identify and represent factors and multiples of whole numbers through 100, and classify numbers as prime or composite.
7.1/7.2/7.4 – NSO 5 Use models and points of reference to compare commonly used fractions.