NEW ZEALAND MATH YEAR 5 – EDmama New Zealand

A. Place Value Fundamentals

A.06. Order numbers up to five digits from least to greatest and greatest to least.
A.07. Round whole numbers to the nearest ten, hundred, thousand, ten thousand, and hundred thousand.
A.08. Apply rounding to estimate values in real-world scenarios.
A.09. Determine whether a number is even or odd using arithmetic rules.
A.10. Represent inequalities on number lines.
A.11. Explore and understand place value systems beyond millions.
A.01. Identify the place value of digits in numbers up to millions.
A.02. Convert numbers between standard and expanded forms.
A.03. Read and write word names for numbers up to millions.
A.04. Recognize and understand Roman numerals.
A.05. Compare numbers up to five digits using , and =.

B. Addition of Whole Numbers

B.01. Add numbers up to four digits using the standard algorithm.
B.02. Use properties of addition (commutative, associative, identity) to simplify calculations.
B.03. Complete input/output tables with addition rules.
B.04. Add three or more numbers up to five digits each.
B.05. Identify addition patterns over increasing place values.
B.06. Solve addition word problems involving numbers up to four digits.
B.07. Add numbers up to five digits using the standard algorithm.
B.08. Solve addition word problems involving numbers up to five digits.
B.09. Fill in missing digits in addition problems.
B.10. Choose numbers that add up to a particular sum.
B.11. Estimate sums by rounding addends to appropriate place values.
B.12. Solve word problems involving estimation of sums.
B.13. Analyze and explain the impact of changing place values on the sum of two numbers.

C. Subtraction of Whole Numbers

C.01. Subtract numbers up to four digits using the standard algorithm.
C.02. Complete input/output tables with subtraction rules.
C.03. Identify subtraction patterns over increasing place values.
C.04. Subtract numbers up to five digits using the standard algorithm.
C.05. Solve subtraction word problems involving numbers up to five digits.
C.06. Subtract across zeros in four-digit numbers.
C.07. Fill in missing digits in subtraction problems.
C.08. Choose numbers that yield a particular difference.
C.09. Estimate differences by rounding minuends and subtrahends to appropriate place values.
C.10. Solve word problems involving estimation of differences.
C.11. Apply subtraction strategies to solve multi-step problems involving addition and subtraction.

D. Multiplication Facts and Properties

D.01. Recall multiplication facts for 7, 8, and 9.
D.02. Recall multiplication facts up to 10.
D.03. Identify the missing factor in multiplication sentences up to 10.
D.04. Determine whether multiplication sentences up to 10 are true or false.
D.05. Use properties of multiplication (commutative, associative, distributive, identity, zero) to simplify calculations.
D.06. Complete input/output tables with multiplication rules.
D.07. Identify multiplication patterns over increasing place values.
D.08. Choose numbers that result in a particular product.
D.09. Multiply numbers ending in zeroes.
D.10. Solve word problems involving multiplication of numbers ending in zeroes.
D.11. Estimate products by rounding factors to appropriate place values.
D.12. Solve word problems involving estimation of products.
D.13. Multiply three numbers together.
D.14. Compare numbers using multiplication.
D.15. Represent inequalities involving multiplication.
D.16. Apply multiplication to solve problems involving scaling and ratios.

E. Multiplication by One-Digit Numbers

F. Multiplication by Two-Digit Numbers

G. Factors, Multiples, and Divisibility

H. Division Facts and Properties

H.01. Recall division facts for 7, 8, and 9.
H.02. Recall division facts up to 10.
H.03. Solve word problems involving division facts up to 10.
H.04. Determine whether division sentences up to 10 are true or false.
H.05. Use properties of division (identity) where applicable.
H.06. Complete division tables.
H.07. Interpret remainders in division problems.
H.08. Complete input/output tables with division rules.
H.09. Choose numbers that result in a particular quotient.
H.10. Divide larger numbers.
H.11. Solve word problems involving division of larger numbers.
H.12. Divide numbers ending in zeroes.
H.13. Estimate quotients by rounding dividends and divisors to appropriate place values.
H.14. Solve word problems involving estimation of quotients.
H.15. Identify division patterns over increasing place values.
H.16. Represent inequalities involving division.
H.17. Connect division to fractions and ratios.

I. Mixed Operations and Problem Solving

I.01. Add, subtract, multiply, and divide whole numbers.
I.02. Solve addition, subtraction, multiplication, and division word problems.
I.03. Determine the order of operations in a mixed operation expression.
I.04. Evaluate expressions involving parentheses, brackets, and braces.
I.05. Estimate sums, differences, products, and quotients in word problems.
I.06. Determine if mixed operation sentences are true or false.
I.07. Solve equations involving one operation.
I.08. Write equations to represent word problems.
I.09. Solve word problems using guess-and-check.
I.10. Use equations to solve addition and subtraction word problems.
I.11. Solve multi-step word problems.
I.12. Solve word problems with extra or missing information.
I.13. Choose numbers that result in a particular sum, difference, product, or quotient.
I.14. Mentally add and subtract numbers ending in zeroes.
I.15. Understand the use of parentheses in mathematical expressions.
I.16. Represent inequalities involving addition, subtraction, multiplication, and division.
I.17. Complete input/output tables with addition, subtraction, multiplication, and division rules.
I.18. Create and solve real-world problems involving multiple operations.

J. Introduction to Fractions

J.01. Review basic fraction concepts (numerator, denominator, whole).
J.02. Identify fractions of a whole using visual models and diagrams.
J.03. Solve word problems involving fractions of a whole.
J.04. Find fractions of a group using visual models and diagrams.
J.05. Solve word problems involving fractions of a group.
J.06. Identify equivalent fractions using area models.
J.07. Graph equivalent fractions on number lines.
J.08. Recognize and generate equivalent fractions.
J.09. Identify patterns of equivalent fractions.
J.10. Write fractions in lowest terms (simplest form).
J.11. Determine a fraction of a number.
J.12. Solve word problems involving fractions of a number.
J.13. Identify mixed numbers from visual representations.
J.14. Write mixed numbers in words.
J.15. Convert between improper fractions and mixed numbers.
J.16. Model and explain the relationship between fractions, decimals, and percentages.

K. Comparing Fractions

K.01. Graph fractions on number lines.
K.02. Compare fractions on number lines.
K.03. Compare fractions with like numerators or denominators.
K.04. Compare fractions with unlike numerators and denominators using various strategies (e.g., common denominators, benchmarks).
K.05. Order fractions with like numerators or denominators.
K.06. Order fractions with unlike numerators and denominators.
K.07. Identify smaller or larger fractions when given a set of fractions.
K.08. Apply fraction comparison to real-world scenarios (e.g., comparing amounts of ingredients).

L. Adding and Subtracting Fractions

M. Introduction to Decimals

M.01. Identify the decimal number represented by a visual model.
M.02. Model decimals and fractions using base-ten blocks and area models.
M.03. Understand decimals expressed in words.
M.04. Identify place values in decimal numbers (tenths, hundredths, thousandths).
M.05. Recognize equivalent decimals.
M.06. Graph decimals on number lines.
M.07. Read and interpret decimal number lines.
M.08. Round decimals to the nearest whole number, tenth, and hundredth.
M.09. Express decimals as fractions and fractions as decimals to understand their relationship.

N. Comparing Decimals

O. Converting Between Decimals and Fractions

P. Comparing Decimals and Fractions

Q. Adding and Subtracting Decimals

Q.01. Add decimals using blocks (visual models).
Q.02. Add decimal numbers using the standard algorithm.
Q.03. Subtract decimals using blocks (visual models).
Q.04. Subtract decimal numbers using the standard algorithm.
Q.05. Solve word problems involving addition and subtraction of decimals.
Q.06. Choose decimals that result in a particular sum or difference.
Q.07. Add three or more decimals.
Q.08. Solve word problems involving addition of three or more decimals.
Q.09. Complete addition or subtraction sentences with decimals.
Q.10. Represent inequalities involving addition and subtraction of decimals.
Q.11. Estimate sums and differences of decimals by rounding.
Q.12. Solve decimal problems using diagrams and models.
Q.13. Apply decimal addition and subtraction to real-world financial situations.

R. Logical Reasoning and Problem Solving

S. Patterns and Sequences

S.01. Identify the next shape in a repeating pattern.
S.02. Complete a repeating pattern.
S.03. Create a repeating pattern.
S.04. Identify the next row in a growing pattern of shapes.
S.05. Complete an increasing number pattern.
S.06. Complete a geometric number pattern.
S.07. Identify and extend number sequences.
S.08. Solve word problems involving number patterns.
S.09. Solve mixed review problems involving number patterns.
S.10. Identify and extend number sequences involving decimals.
S.11. Describe the rule governing a given pattern or sequence.

T. Money and Financial Literacy

T.01. Count coins and notes up to a $5 note.
T.02. Compare money amounts.
T.03. Round money amounts to the nearest ten cents.
T.04. Solve word problems involving rounding to the nearest ten cents.
T.05. Round money amounts to the nearest dollar or more.
T.06. Add and subtract money amounts.
T.07. Calculate making change.
T.08. Use price lists to solve problems involving money.
T.09. Plan a budget and make financial decisions within constraints.

U. Units of Measurement (Metric)

U.01. Read a thermometer and interpret temperature readings.
U.02. Determine a reasonable temperature for various situations.
U.03. Choose the appropriate metric unit of measure for a given object or quantity.
U.04. Determine which metric unit of length is appropriate for measuring different objects.
U.05. Compare and convert metric units of length (mm, cm, m, km).
U.06. Determine which metric unit of mass is appropriate for measuring different objects.
U.07. Compare and convert metric units of mass (mg, g, kg).
U.08. Determine which metric unit of volume is appropriate for measuring different liquids.
U.09. Compare and convert metric units of volume (mL, L).
U.10. Solve problems involving metric mixed units (e.g., 1.5 km = ? m).
U.11. Estimate measurements in metric units.

V. Time

V.01. Convert between different units of time (seconds, minutes, hours, days, weeks, months, years).
V.02. Add and subtract mixed time units (e.g., 2 hours 30 minutes + 1 hour 45 minutes).
V.03. Calculate fractions of time units (e.g., 1/2 hour = ? minutes).
V.04. Calculate elapsed time.
V.05. Find start and end times in multi-step word problems.
V.06. Interpret transportation schedules.
V.07. Identify and extend time patterns.
V.08. Solve problems involving time zones.

W. Two-Dimensional Figures

W.01. Identify whether a given figure is a polygon.
W.02. Count the number of sides in polygons.
W.03. Identify two-dimensional figures based on their properties.
W.04. Distinguish between lines, line segments (intervals), and rays.
W.05. Identify parallel, perpendicular, and intersecting lines.
W.06. Compare angles to a right angle (greater than, less than, or equal to).
W.07. Classify angles as acute, right, obtuse, or straight.
W.08. Classify triangles based on their angles (acute, right, obtuse) and sides (scalene, isosceles, equilateral).
W.09. Calculate the perimeter of polygons.

X. Symmetry and Transformations

Y. Three-Dimensional Figures

Y.01. Identify three-dimensional figures (cube, rectangular prism, sphere, cone, cylinder, pyramid).
Y.02. Count the number of vertices, edges, and faces of three-dimensional figures.
Y.03. Identify the faces of three-dimensional figures.
Y.04. Identify three-dimensional figures based on their properties.
Y.05. Identify the bases of three-dimensional figures.
Y.06. Identify nets of three-dimensional figures.
Y.07. Identify front, side, and top views of three-dimensional figures.
Y.08. Relate two-dimensional shapes to the faces of three-dimensional objects.

Z. Geometric Measurement: Perimeter, Area, and Volume

Z.01. Calculate the perimeter of various shapes.
Z.02. Determine missing side lengths of a polygon given its perimeter.
Z.03. Calculate the area of figures made of unit squares.
Z.04. Select figures with a given area.
Z.05. Select two figures with the same area.
Z.06. Create figures with a given area.
Z.07. Find the area or missing side length of a rectangle given its area.
Z.08. Solve word problems involving area and perimeter.
Z.09. Understand the concept of volume.
Z.10. Find the volume of rectangular prisms by counting unit cubes.
Z.11. Relate volume to the number of layers and area of the base.

AA. Data and Graphs

AA.05. Create bar graphs from given data.
AA.06. Interpret information presented in line plots.
AA.07. Create line plots from given data.
AA.08. Interpret information presented in frequency charts.
AA.09. Create frequency charts from given data.
AA.10. Interpret information presented in stem-and-leaf plots.
AA.11. Create stem-and-leaf plots from given data.
AA.12. Interpret and analyze circle graphs (pie charts).
AA.13. Choose the best type of graph to represent a given set of data.
AA.14. Solve problems using data presented in various graph types.
AA.01. Read and interpret data presented in a table.
AA.02. Interpret information presented in line graphs.
AA.03. Create line graphs from given data.
AA.04. Interpret information presented in bar graphs.

BB. Coordinate Plane

CC. Probability and Statistics

CC.01. Determine if an event is more, less, or equally likely to occur.
CC.02. Classify events as certain, probable, unlikely, or impossible.
CC.03. Calculate the probability of a simple event.
CC.04. Make predictions based on probability.
CC.05. Determine the number of possible combinations in a given situation.
CC.06. Calculate the mean (average) and mode of a data set.
CC.07. Interpret charts to find the mean and mode.
CC.08. Understand and calculate the range of a data set.

Course Content

A. Place Value Fundamentals

A.06. Order numbers up to five digits from least to greatest and greatest to least.

A.07. Round whole numbers to the nearest ten, hundred, thousand, ten thousand, and hundred thousand.

A.08. Apply rounding to estimate values in real-world scenarios.

A.09. Determine whether a number is even or odd using arithmetic rules.

A.10. Represent inequalities on number lines.

A.11. Explore and understand place value systems beyond millions.

A.01. Identify the place value of digits in numbers up to millions.

A.02. Convert numbers between standard and expanded forms.

A.03. Read and write word names for numbers up to millions.

A.04. Recognize and understand Roman numerals.

A.05. Compare numbers up to five digits using , and =.

B. Addition of Whole Numbers

B.01. Add numbers up to four digits using the standard algorithm.

B.02. Use properties of addition (commutative, associative, identity) to simplify calculations.

B.03. Complete input/output tables with addition rules.

B.04. Add three or more numbers up to five digits each.

B.05. Identify addition patterns over increasing place values.

B.06. Solve addition word problems involving numbers up to four digits.

B.07. Add numbers up to five digits using the standard algorithm.

B.08. Solve addition word problems involving numbers up to five digits.

B.09. Fill in missing digits in addition problems.

B.10. Choose numbers that add up to a particular sum.

B.11. Estimate sums by rounding addends to appropriate place values.

B.12. Solve word problems involving estimation of sums.

B.13. Analyze and explain the impact of changing place values on the sum of two numbers.

C. Subtraction of Whole Numbers

C.01. Subtract numbers up to four digits using the standard algorithm.

C.02. Complete input/output tables with subtraction rules.

C.03. Identify subtraction patterns over increasing place values.

C.04. Subtract numbers up to five digits using the standard algorithm.

C.05. Solve subtraction word problems involving numbers up to five digits.

C.06. Subtract across zeros in four-digit numbers.

C.07. Fill in missing digits in subtraction problems.

C.08. Choose numbers that yield a particular difference.

C.09. Estimate differences by rounding minuends and subtrahends to appropriate place values.

C.10. Solve word problems involving estimation of differences.

C.11. Apply subtraction strategies to solve multi-step problems involving addition and subtraction.

D. Multiplication Facts and Properties

D.01. Recall multiplication facts for 7, 8, and 9.

D.02. Recall multiplication facts up to 10.

D.03. Identify the missing factor in multiplication sentences up to 10.

D.04. Determine whether multiplication sentences up to 10 are true or false.

D.05. Use properties of multiplication (commutative, associative, distributive, identity, zero) to simplify calculations.

D.06. Complete input/output tables with multiplication rules.

D.07. Identify multiplication patterns over increasing place values.

D.08. Choose numbers that result in a particular product.

D.09. Multiply numbers ending in zeroes.

D.10. Solve word problems involving multiplication of numbers ending in zeroes.

D.11. Estimate products by rounding factors to appropriate place values.

D.12. Solve word problems involving estimation of products.

D.13. Multiply three numbers together.

D.14. Compare numbers using multiplication.

D.15. Represent inequalities involving multiplication.

D.16. Apply multiplication to solve problems involving scaling and ratios.

E. Multiplication by One-Digit Numbers

E.01. Multiply one-digit numbers by two-digit numbers.

E.02. Multiply one-digit numbers by two-digit or three-digit numbers using area models.

E.03. Multiply one-digit numbers by three-digit numbers.

E.04. Multiply one-digit numbers by larger numbers.

E.05. Use estimation to check the reasonableness of products.

F. Multiplication by Two-Digit Numbers

F.01. Use the box method (area model) for multiplication.

F.02. Use lattice multiplication.

F.03. Multiply a two-digit number by a two-digit number, completing missing steps in the process.

F.04. Multiply a two-digit number by a two-digit number.

F.05. Solve word problems involving multiplication of two-digit numbers.

F.06. Compare and contrast different multiplication methods, explaining their efficiency.

G. Factors, Multiples, and Divisibility

G.01. Identify factors of a given number.

G.02. Determine whether a number is prime or composite.

G.03. Choose multiples of a given number up to 12.

G.04. Apply divisibility rules for 2, 3, 5, 6, 9, and 10.

G.05. Solve word problems involving divisibility rules.

G.06. Use prime factorization to find the greatest common factor (GCF) and least common multiple (LCM) of two numbers.

H. Division Facts and Properties

H.01. Recall division facts for 7, 8, and 9.

H.02. Recall division facts up to 10.

H.03. Solve word problems involving division facts up to 10.