MATHEMATICS

GUIDELINES

READINESS SKILLS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

CONCRETE EXPERIENCES WITH NUMBER CONCEPTS

Applied and maintained from material presented in curriculum for Grades 1 – 3.

Guidelines for Grades 1 – 3.

SETS AND THEIR NUMBERS

Maintain concepts presented in Grades 1 – 3. Apply to whole numbers.

D

NUMBER SENSE

M-4.1: The students will continue to develop a sense of number – meaning and value.

M-4.2: The students will understand place value through millions.

M-4.3: The students will read and write 9-digit numerals in standard and written form.

units

tens

hundreds

thousands

ten thousands

hundred thousands

millions

number

numeral

digit

3,572,402

Emphasize comma as an aid in reading numbers.

There are three hundred sixty-five thousand people living in Smalltown. Write this in numbers.

Language Arts, Real Life Skills: Conduct a newspaper or news magazine scavengers hunt for large number. Do an oral report explaining the use of each.

Study Skills: Locate lists of numbers in a reference book or almanac. Discuss the use of large numbers for topics such as area, population, etc.

COMPARING AND ORDERING SETS AND NUMBERS

Ongoing maintenance from previous work. Continue to compare numbers using the appropriate signs: >, <, =. Have the students speak in sentences when comparing. Gradually include higher level numbers. Challenge students to include higher level thinking skills.

2345 < 3254 235 + 429 _____ 700 3 x 33 _______21 x 4

NCTM ADDENDA SEREIS, GRADE 4 BOOK

READINESS SKILLS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

READING NUMBERS

WRITING NUMERALS

M-4.4: The students will continue to develop skill in reading and writing of numbers.

STRESS: the correct formation of numerals.

4876

Pitfalls to avoid:

- putting curves in fours and sevens;

- beginning numerals on the base line rather than on the top line;

- making fractions two spaces high. Fractions should be written in one space:

1 1

4 7

Handwriting: Teach correct method for formation of numerals.

NUMBER PATTERNS

M-4.5 Students will discover and complete number patterns.

skip counting

multiples

patterns

Multiple Counting –

5, 10, 15, 20, 25, 30, 35, 40….

Skip Counting –

3, 8, 13, 18, 23, 28, 33, 38

Mrs. Jones made a payment on her bill on August 2. She must make another payment in three weeks. When will she make the next payment?

(August 23)

Real Life: time schedules, reading calendars

READINESS SKILLS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

ORDINAL NUMBERS

M-4.6: The students will distinguish between cardinal and ordinal numbers.

cardinal

ordinal

Emphasize:

Quantitative value- cardinal

Positional value - ordinal

Cardinal – 1

Ordinal – 1st

Who is first in line?

There is one God.

What is the first great Commandment?

Religion: Use numbers in the “catechism clock” to remind students of important faith facts: one God, two great commandments, three persons in God, four gospel writers, five wise virgins, six works of mercy, seven commandments, eight beatitudes, nine choirs of angels, ten commandments, eleven faithful apostles, twelve tribes of Israel.

UNDERSTAND AND USE SYMBOLS

M-4.7: The students will review and use the following mathematical symbols:

+, -, x, ¸, <, >, =, ¹

WHOLE NUMBER CONCEPTS, NUMBER RELATIONS – LEVEL 4

Exponents/Powers - introduced

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

D

PLACE VALUE

Refer to NUMBER SENSE in READINESS SECTION of Guidelines for scope of this skill.

EXPANDED NOTATION

M-4.8: The students will write nine-digit numerals using expanded notation.

expanded notation

Write 1,947,268 using expanded notation.

1,947,268 = 1,000,000,+ 900,000 + 40,000 + 7,000 + 200 + 60 + 8

Handwriting, Math: To assist the students to align numbers correctly when adding/subtracting, turn notebook/paper sideways:

1 0 0 0 0 0 0

8 0 0 0 0 0

4 0 0 0 0

7 0 0 0

8 0 0

2 0

1 8 4 7 8 2 5

D

MONEY

M-4.9: The students will read, write, and use dollar and cent notation.

dollar

cent

$59.76

Read: fifty-nine dollars and seventy-six cents.

Real Life, Consumer topics

NUMBER CONCEPTS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

D

ROUNDING

M-4.10: The students will round numbers to the nearest thousand, ten thousand, and hundred thousand.

M-4.11: The students will round money to the nearest dollar.

round

compatible

Round 427,268 to the nearest:

thousand: 427,000

ten thousand: 430,000

hundred thousand: 400,000

-------------------------------------

$12.49 rounded to the nearest dollar is $12.00.

Social Studies, Science:

using large numbers

Consumer Topics: estimating cost, amounts needed.

ESTIMATING

M-4.12: The students will use rounding and compatible numbers as aids to estimation.

The population of Largetown is 542,768. About how many hundred thousand people live there?

FACTORS

COMMON FACTORS

FACTORIZATION AND GREATEST COMMON FACTOR

M-4.13: The students will understand the concept of factor and will identify factors common to more than one multiple; they will become familiar with the term greatest common factor.

factor

common factor

greatest

common factor

factorization

The factors of 12 are: 1 2

12 6

The factors of 15 are: 1 3

15 5

1 and 3 are on both lists of factors, so 1 and 3 are common factors of 12 and 15. 3 is the greatest common factor.

List the common factors of 16 and 24.

Which is the greatest common factor?

Real Life: Identify common factors among family members; name, eye color, complexion, etc.

Social Studies: Identify factors common to city and state government.

Reading: Compare and contrast; note similarities and differences.

NUMBER CONCEPTS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

D

MULTIPLES

M-4.14: The students will become familiar with the concepts of multiple and lease common multiple.

multiple

least common multiple

Multiples of 6:

6, 12, 18, 24,30,36, 42, 48, 54…

Multiples of 8:

8, 16, 24, 32, 40, 56….

Common multiples of 6 and 8 are 24 and 48. The least common factor is 24.

Study Skills: use a memory device such as

A factor is equal to or fewer; a multiple is equal to or more.

ROMAN NUMERALS

M-4.15: The students will read and write Roman Numerals through 100.

Roman numeral

Note: a numeral of lesser value preceding one of greater value indicates subtraction.

Joan wants to number the pages of her notebook using Roman Numerals. What numerals will she place on pages 38 to 42?

Real Life: clocks, outline writing.

PRIME NUMBERS

COMPOSITE NUMBERS

M-4.16: The students will explore the concept of prime numbers and composite numbers.

prime number

composite number

2, 3, 5, 7, 11, and 13 are prime numbers.

4, 6, 8, 9, 10 are composite numbers.

The number 1 is neither prime nor composite.

A prime number has exactly two factors: 1 and itself.

A composite number has more than two factors.

NUMBER CONCEPTS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

COMPARING NUMBERS

USE SYMBOLS TO SHOW NUMBER RELATIONS

M-4.17: Using symbols the students will compare numbers.

< less than

> greater than

= equal to

most

fewer

fewest

1324 > 1243

(see examples in readiness section of guidelines)

Tina read 384 pages of a book over the summer vacation. Hilda read 2 books – one with 231 pages and one with 153 pages. Who read more? (neither)

M

NUMBER LINE

M-4.18: The number line is used as a tool for comparing numbers and for the development of the addition and subtraction concepts. Refer to these concepts for further development.

I

FRACTIONS

M-4.19: The students will define fractions as equal parts of a whole.

M-4.20: The students will determine a pair of numbers or the missing element of a pair when given a relation or rule, and will determine the relation or rule of given pairs of numbers.

M-4.21: The students will use models to compare fractions and to identify equivalent fractions.

fraction

numerator

denominator

equivalent fraction

1 numerator

4 denominator

1 = 2 .

2 4

A Kit-Kat bar

Can be divided into four equal parts. Each part is 1/4.

Use fraction strips or fraction bars to show that

1/2 = 2/4

Real Life: Egg cartons, candy bars, etc.

OPERATIONS – LEVEL 4

WHOLE NUMBER OPERATIONS

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

USE CONCRETE OBJECTS TO MODEL OPERATIONS

OPERATIONS INTRODUCED AND DEVELOPED IN PROBLEM SOLVING/

REAL LIFE CONTEXT

USE SYMBOLS FOR OPERATIONS

M-4.22: The students will use concrete objects to model operations.

M-4.23: The students will develop understanding of concepts through a problem-solving context.

M-4.24: The students will understand the meaning of and will use symbols for all operations.

M-4.25: The students will select appropriate symbol ( +, -, x, ¸, >, <, =) to make a mathematical statement true.

add

addition

operation

plus

plus sign +

sum addend equals

subtract

subtraction

minuend

subtrahend

difference

minus sign -

multiply

multiplication

multiplier

multiplicand

product

factor

multiplication sign x

divide

division

divisor

dividend

quotient

division sign ¸

Students should have adequate practice in all operations at this level. Important factors to take into consideration:

1. Practice should include both computational practice as well as problem-solving practice.

2. Practice should include examples given in both horizontal and vertical notation.

3. Missing addends and factors need practice.

4. Ample practice with zero as a placeholder should be provided.

5. Care should be taken that the students align the computational examples correctly.

Real Life: Careers in business, ordering, inventory

Study Skills: Make use of large numbers from an almanac/atlas.

Vocabulary: prefixes- sub-, ad-, multi-, di-

Technology: use calculator to verify answers.

Language Arts: Have the students write original word problems based on computational examples.

OPERATIONS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

ADD MULTI-DIGIT NUMBERS

M-4.26: Review the addition of multi-digit numbers. Extend to six digits (with regrouping). Apply

to problem solving situations.

PROPERTIES OF ADDITION

M-4.27: The students will continue to develop an understanding of the commutative, associative, and identity properties of addition.

commutative

property

order

associative

grouping

identity property

46 + 82 = 128

82 + 46 = 128

46 + 82 = 82 + 46

(18 + 9) + 25 = 52

18 + (9 + 25) = 52

Ellen had a box of 46 books and another box of 82 books. Will the order in which she unpacks them affect the total number of books?

18 boys and 9 girls were in the gym. 25 more students came in. How many were there then?

Real Life: Inventories, trains going different routes to the same destination.

M

ESTIMATING

SUMS

M-4.28: Apply estimation skills. Use as an aid in checking answers.

SUBTRACT MULTI-DIGIT NUMBERS

M-4.29: Review the subtraction of multi-digit numbers. Emphasize subtraction as the inverse of

Addition. Extend concept to include 9-digit numbers (with and without regrouping).

Include numbers with zeroes as placeholders. Apply to problem solving situations.

MISSING ADDENDS

M-4.30: The student will be able to identify a missing addend in a given number sentence.

addend

8 + ____ = 11

Sally had 8 Barbies before her party. After her party, she had 11. How many Barbies did she receive for her birthday?

OPERATIONS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

ESTIMATING DIFFERENCES

M-4.31: Apply estimation skills to all areas of subtraction. Use as an aid in checking answers.

MULTIPLICATION

M-4.32: The students will multiply:

-- 4 and 5 digit numbers by 1-digit multipliers;

--by multiples of one hundred without regrouping

--3 and 4 digit numbers by 2 -digit multiplier

M-4.33: The students will apply the commutative, associative, distributive, and identity properties to multiplication.

Multiplication Rule:

Product =

factor x factor

1482

x 8

1856

x 10

350

923

x 64

3692

55380

59072

84 students in the fourth grade each brought an average of $17 for the missions last year. How much money did the fourth grade give to the missions?

Real Life

ESTIMATING PRODUCTS

M-4.34: Apply estimation to all areas of multiplication. Use as an aid in checking answers.

MISSING FACTORS

M-4.35: The student will be able to identify a missing factor in a given number sentence.

factor

7 x ___ = 35

There are seven rows of desks in a classroom. If there are 35 desks in all, how many desks are in each row?

OPERATIONS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

D

DIVISION

1-DIGIT DIVISORS

2-DIGIT DIVISORS

REMAINDERS

M-4.36: The students will divide a 4-digit dividend by a

1-digit divisor with and without remainders.

M-4.37: The students will divide a 4-digit dividend by a

2-digit divisor with and without remainders.

M-4.38: The students will interpret remainders in a division problem.

divisor

dividend

quotient

remainder

¸ )

Emphasize division as inverse of multiplication.

*Teacher alert

1. Provide adequate practice with zero.

2. Remainder is not part of the quotient, since it is not an answer to a division question.

1230 r 7

8)9847

-8

-16

-24

-0

204

22) 4488

-44

-0

-88

There were a total of 9,848 library books in each of the 8 schools in the Springfield area. If each had the same number, how many were in each library?

Suppose 16 schools shared these books, how many would each have?

Real Life: Consumer topics

Mathematics: Operations, problem solving, measurement, geometry

OPERATIONS – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATION

RESOURCES

I

ESTIMATING

QUOTIENTS

M-4.39: Estimating quotients, per se, is not a developed skill at this level. However, the students should use the skill of estimating products to check on the reasonableness of an answer in division. (e.g. rounding off the obtained quotient and the divisor and multiplying to find an approximate dividend.

D

FRACTIONS

M-4.40: The students will add and subtract fractions with like denominators.

fraction

numerator

denominator

3 + 1 = 4

5 5 5

5 - 2 = 3

7 7 7

Marsha’s birthday cake was cut into 12 slices. 5 of the slices were eaten. Write a fraction sentence to show this.

12 - 5 = 7

12 12 12

Real Life: recipes, carpentry, packaging done in multiples

USE DOLLAR AND CENT NOTATION IN ALL

OPERATIONS

M-4.41: The students will use dollar and cent notation in all operations.

dollar

cent

decimal point

$46.95 x 3

$12.87 - $7.29

$4.85 ÷ 5

Be sure to give examples in both horizontal and vertical notation.

Juanita spent the following amounts at

K–Mart: $2.98, $5.34, $0.25, and $1.99. Not counting the tax, what is her bill?

Real Life: Shopping, paying bills, using coupons, earning wages, saving money

PROBLEM SOLVING – LEVEL 4

SEQUENCE

SKILL

OBJECTIVE

VOCABULARY

EXAMPLE

PROBLEM SOLVING EXAMPLE

CONNECTIONS,

INTEGRATIONS

RESOURCES

USE A PLAN FOR PROBLEM SOLVING

Understand the question

Plan: Choose a

correct strategy.

M-4.42: The students will read and identify the facts given and questions asked in the problem.

M-4.43: Students will select an appropriate strategy and operation

read

identify

problem

facts

question

“Math shorthand”

Fà Facts

?à Question

number sentence

operation

plus

minus

sum

difference

greater

fewer

equation

model

picture

table

diagram

Ali Baba had 40 thieves. Three went north, two went south, four went east. The thieves that went north and south were arrested. How many thieves did Ali Baba have then?

Fà 40 t

Fà 3 n

Fà 2 s

Fà 4 e

Fà n and s arrested.

Qà ? t remaining

After strategies are taught, children might choose from the f