Math unit plan for missing numbers

MATHEMATICS UNIT PLAN

SETEMBER

Week One: Routines and procedures

Week two

Subject: Mathematics

Topics: Missing Numbers in Addition, Missing Numbers in Subtraction, Missing Numbers in Multiplication,
Missing Numbers in Division,

Previous Knowledge:

Students are able to read and write numbers up to million, and have been introduced to a number line in lesson
9.

Objectives:

Through use of direct instruction, Class discussion and practice, students will be able to:

Lesson 03
1. Use subtraction to find a missing addend in an addition problem.
2. Check their answer to a missing number in an addition problem by using the answer in place of
the letter in the original problem.
3. Find the missing minuend in a subtraction problem by adding the subtrahend and the difference.
4. Find the missing subtrahend in a subtraction problem by subtracting the difference from the
minuend.
5. Check their answer to a missing number in a subtraction problem by using the answer in place of
the letter in the original problem.
Lesson 04
6. Use division to find a missing factor in a multiplication problem.
7. Find the missing dividend in a division problem by multiplying the divisor and the quotient.
8. Find the missing divisor in a division problem by dividing the dividend by the quotient.
Lesson 05
9. Take steps in order from left to right in a problem with more than one addition or subtraction
step.
10. Take steps in order from left to right in a problem with more than one multiplication or division
step.
11. Do the work within parentheses first when solving a problem with more than one step.
12. Identify and use the associative property of addition and the associative property of
multiplication.
13. Perform the operations above the bar and below the bar before dividing in a division problem
with a bar.

Concepts:

- We can find a missing addend by subtracting the known addend from the sum.
Example: 12 + m = 31 - solution: 31 – 12 = 19, therefore the m = 19
- We can find a missing minuend (first number in a subtraction problem) by adding the other two
numbers. Example: w – 16 = 24 – solution 16 + 24 = 40, therefore w = 40
- We can find a missing subtrahend (second number in a subtraction problem) by subtracting the
difference from the minuend. Example: 236 – y = 152 – solution 236 – 156 = 84, therefore y = 84
- We can find a missing factor by dividing the product by the known factor. Example: A x 6 = 72 –
solution: 72 ÷ 6 = 12, therefore A = 12
- We can find the missing dividend (the number inside the division box) by multiplying the other two
numbers. We can find either the divisor or quotient (the numbers outside the box) by dividing.
- When there is more than one addition or subtraction step within a problem, we take the steps in order
from left to right. In this problem we first subtract 4 from 9. Then we add 3. 9 – 4 + 3 = 8
- If a different order of steps is desired, parentheses are used to show which step should be taken first. In
the problem below, we first add 4 and 3 to get 7. Then we subtract 7 from 9. 9 – (4 + 3) =2

Skills:

- Ordering mathematical operations
- Finding missing numbers in multiplication and division
- Finding missing numbers in addition and subtraction.
- Using appropriate vocabulary for mathematical arithmetic operations.

Attitudes:

- Awareness that math is used in our daily life.
- Appreciation for numbers.
- Respect for others and their ideas.
- Cooperation as students work in groups.

Teaching/Learning Strategies:

Day One

- Students perform warm-up activities – Addition Facts, Mental Math, Problem Solving
- Present and addition problem to students.
- Have them cover one addend and then the next with their fingers.
- Discuss with students what steps they would do to find any of the missing addends they covered with
their fingers.
- Listen to students responses and acknowledge anyone who shows the correct steps.
- Model out for children the correct steps to solve these problems.
- Allow students to practice and to assess their understanding of it.
- Next, present a subtraction problem for students on the white board.
- Ask them to cover the subtrahend with their fingers and describe what would they do to find that
missing number.
- Listen to students how they would go about solving this problem. Then elaborate of provide correct
steps for children to solve this type of problem.
- Now have students do likewise with the minuend and repeat the last three steps with them.

- Provide enough examples for students and practice to assess their understanding of this problem.
- Have children work on the mixed practice section of their Saxon Math books to reinforce previous
concepts covered and the present ones.
-

Day two:

- Students perform warm-up activities – Addition Facts, Mental Math, and Problem Solving.
- Present a multiplication fact to students. Ask them to cover any of the factors with their fingers.
- Have them come up with a way of describing how they can use the two uncovered numbers to find the
covered number.
- Listen to children‟s responses and carry out from suggestions they have offered.
- Instruct them how to go about working this type of problem.
- Provide them with different examples and allow the class to participate in completing the steps of each
example given.
- Have students practice some problems and assess their understanding of these problems.
- Do likewise with a division problem. Have students covered all the three numbers in division problem
and offer ideas how we could find the covered number.
- Follow on from suggestion given by students and show them step by step how to go about solving these
problems.
- Have students work problems of the practice section of this lesson.
- Check work and go over problems where children had difficulty.
- To reinforce past concepts covered and these ones, have children work on the mixed practice of the
lesson.

Day three:

- Write the following problems for students on the white board: 9 – 4 + 3 = 4
- Ask students try to work out this problem.
- Invite anyone who thinks has the correct answer to come to the board and write it.
- Acknowledge the students if he got it correct, if not, congratulate him/her for trying.
- Next, instruct students the steps taken to work out such problem.
- Provide them with problems where parentheses are used. Show clearly to students how to solve this type
of problem. Involve the class in finding the solution to the problem.
- Provide students with other examples to achieve understanding of the problems.
- Then have them work on the practice section of the lesson to assess their understanding of this lesson.

Day Four:

- Students will be tested on the last five lessons by doing the mixed practice of lesson 5.

Assessment Strategies:

- Oral participation
- Lesson practices
- Tests

Reference/Materials:

- Saxon Math 7/6 Teacher Resource Book – page 12 – 22
- Saxon Math 7/6 - Students Book – Lesson 3 - 5.
- Markers
- White board

Evaluation:

Week Three


Lesson Topic: Fractional Parts; Lines, Segments, Rays; Linear Measurement.

Class: Standard V

Previous Knowledge:

Students are able to identify numerator and denominators.

Objectives:

Through use of direct instruction, Class discussion and practice, students will be able to:
Lesson 06
1. Use a fraction to name part of a whole.
2. Use a fraction to use part of a group.
3. Divide a number into equal parts to find a fractional part of that number.
Lesson 07
1. Identify line, segments, and rays.
2. Use an inch rule to measure line segments to nearest quarter of an inch.
3. Use a centimetre ruler to measure line segments in centimetres and millimetres.

Reference / Materials:

- Saxon Math 7/6 Teacher Resource Book – page 23 - 30
- Saxon Math 7/6 - Students Book – Lesson 6 - 7
- Markers
- Bristol board
- ruler
- strips of paper

Concepts:

- Fractions – is written with two numbers and a fraction bar.
- Denominator – is the bottom number, shows the numbers of equal parts in the whole.
- Numerator – the top number shows the number of the parts being represented.
- A mathematical line has no endpoints. We use arrowheads to indicate a lines unending quality.
- A segment is part of a line and has two endpoints.
- A ray has one endpoint. We represent it with one arrowhead.

Skills:

- Defining skills as they define mathematical vocabulary.
- Identifying skills as students identify numerator, denominator, lines, rays, etc ...

Attitudes:


Teaching / Learning Strategies:

Day One:

- Write the following terms on the board fraction, denominator and numerator.
- Elicit from students what each term means.
- Next, use a picture fraction and number fraction to explain each one to students.
- Show students examples of fractions of a whole and of fractions of a group. Make sure students know
the different between the two of them.
- As a class study and workout the examples found in the book.
- Have students work on practice set a – h.
- Check work and go over problems where children had difficulty.

Day two:

- Draw on the white board an illustration of a line, line segment, rays and endpoints.
- Have students examine the illustrations and state what differences they observe in the illustrations.
- As a class read the information on the book, and discuss. Have students write notes in their exercise
book.
- Discuss the difference between each illustration shown.
- Distribute strips of paper to students. With the use of their rulers students will draw inch marks on the
paper.
- Next, have students draw half inch marks on their paper. Tell them to estimate the distance and draw the
half inch mark slightly shorter than the inch marks.

- Tell them to show quarter marks by estimating the have the distance between each half inch.
- Have students turn their attention to the centimetre ruler now and explain the different measurements,
that is, centimetre and millimetres.
- Have students compare the inch ruler and the centimetre ruler and discuss what differences are
observed.
- Work the examples on the book to practice measuring with an inch ruler and a centimetre ruler.
- Students work on practice set while teacher walks around checking students work.
- Have children work on the mixed practice section of their Saxon Math books to reinforce present and
past concepts covered.

Wednesday: Fence decoration

Thursday: Children‟s rally

Friday: Independence Day Holiday

- Drills
- Practice sets
- Illustrations of inch ruler and centimetre ruler

Evaluation:

Week four


Lesson Topic: Lines, Segments, and Rays; Linear Measure; Perimeter, the number line, ordering and
comparing; Sequence and Scale

Class: Standard V

Previous Knowledge:

Students have used a ruler before and can identify the symbols used to compare numbers.

Objectives:

Through the use of rulers, diagrams, teacher direct instruction and class discussion, students will be able to:
Lesson 7
1. Identify lines, segments, and rays.

2. Use an inch ruler to measure line segments to the nearest quarter inch.
3. Use a centimetre ruler to measure line segments in centimetres and millimetres.
Lesson 8
4. Recognize that the total distance around the classroom is perimeter of the classroom.
5. Find the perimeter of a shape by adding the lengths of the shape‟s sides.
6. Find the length of a side of a square when the perimeter of the square is known.
Lesson 9
7. Use number line to order numbers from least to greatest.
8. Use symbols >,<, and = to compare two numbers.
9. Find the value of two expressions and compare them using the symbols.
Lesson 10
10. Identify addition and multiplication sequence.
11. Identify even and odd numbers.
12. Find the value of marks on a scale.
13. Read the number indicated on a scale.
Concepts:

- Endpoints points at which segments end.
- Line – a straight collection of points extending in opposite direction without end.
- Ray – a part of a line that begins at a point and continues without end in one direction.
- Segment – a part of a line with two distinct endpoints.
- Perimeter - the distance around a closed flat shape.
- Counting numbers - The numbers used to count: the members of the set (1, 2, 3, 4, 5, …). Also
called natural numbers.
- Negative numbers – numbers less than zero.
- Number line - a linfor representing and graphing numbers. Each point on the line corresponds to a
number.
- Whole numbers: The members of the set (0, 1, 2, 3, 4, …)
- Celsius scale - a scale used on some thermometers to measure temperature.
- Even numbers can be divided by 2 without a remainder.
- Odd numbers have a remainder of 1 when divided by 2.
- Fahrenheit scale is used on some thermometers to measure temperature.
- A scale displays numbers with an indicator to show the value of a certain measure.
Skills:

- Comparing skills as they compare numbers.
- Add and division skills as they find perimeter, length or width.
- Identifying skills as they identify the rule for an addition or multiplication sequence.
- Reading and finding skills as they find the value of the marks on a scale.

Attitudes:

- Respect for others and their ideas

Teaching Strategies/ Students Activities:

Monday:

- Draw on the white board an illustration of a line, line segment, rays and endpoints.
- Have students examine the illustrations and state what differences they observe in the illustrations.
- As a class read the information on the book, and discuss. Have students write notes in their exercise
book.
- Discuss the difference between each illustration shown.
- Distribute strips of paper to students. With the use of their rulers students will draw inch marks on the
paper.
- Next, have students draw half inch marks on their paper. Tell them to estimate the distance and draw
the half inch mark slightly shorter than the inch marks.
- Tell them to show quarter marks by estimating the have the distance between each half inch.
- Have students turn their attention to the centimetre ruler now and explain the different measurements,
that is, centimetre and millimetres.
- Have students compare the inch ruler and the centimetre ruler and discuss what differences are
observed.
- Work the examples on the book to practice measuring with an inch ruler and a centimetre ruler.
- Students work on practice set while teacher walks around checking students work.
- Have children work on the mixed practice section of their Saxon Math books to reinforce present and
past concepts covered.

Tuesday:

- Elicit from students the definition of perimeter. Together discuss the definition and use examples to
clarify the concept.
- Have students draw a rectangle and go out and walk the perimeter of the volleyball court and count their
steps. Tell them to write the amount of steps for each side and write on the rectangle drawn in their
exercise books.
- Once students are finished they will go back to the class and answer the questions on page 35 of their
books.
- Have students use rulers and measure their exercise books and their Saxon Math books and then find the
perimeter of each.
- Discuss answers and steps taken to arrive at them.
- Discuss examples in the book and ask students to explain how we know that the lengths of the unlabeled
sides of the rectangle are 2 cm and 3 cm. Listen to students‟ responses and discuss.
- Students will work on practice set a-f. Once they are done we will review as a class.
- Students will start to work on the thirty questions found in Mixed Practice Set. They will complete this
exercise for homework.

Wednesday:

- Present a number line to students. Ask them if they know how we call this diagram. If they don‟t know,
tell them how we call it.
- Have students observe it and tell you (the teacher) what it has (a line, marks, and numbers).
- Tell them that a number line may be numbered with different types of numbers that is, counting
numbers (whole numbers including zero), negative numbers, etc.

- Have students observe that this line is made up of whole numbers and negative numbers. Discuss with
them how numbers increase in value when we move to the right side of the number line and decrease in
value when we move to the left.
- Use example 1 from the book to show students how to arrange numbers from least to greatest using a
number line.
- Explain to students that we can use a number line to compare the value of numbers.
- Talk about the symbols used to compare the value of numbers.
- Discuss the examples given on the book along with students. Probe students through questioning to
assess their understanding of the examples being discussed.
- Explain to them step by step what we do when comparing two numbers of different values:
 Check if the numbers have the same amount of digits.
 Compare its place value one by one until you arrive at the number with the greatest
value.
 Once found, decide what symbol should be used (> greater, < less than). If the number is
the same, then you use an equal sign.
- Students will work on practice set from A – F. Teacher will walk around checking students work and
aiding those who need help.
- Once students are done with practice set they will then start working on mixed practice 1 - 30.
Thursday:

- Write the following two sequences on the board:
a. 5, 10, 15, 20, 25, …
b. 5, 10, 20, 40, 80, …
- Ask students if they know how we call these sets of numbers – sequences.
- Tell students that a sequence is an ordered list of numbers, called terms.
- Discuss the two types of sequences presented.
- Students analyze the sequences and find out what rule was used to form both sequences presented.
- Guide students to arrive to a conclusion.
- Explain to students that sequences follow a rule. Sometimes it may be by adding the same number to the
term. In this case we did that in the first sequence; hence, we have an addition sequence. In the second
sequence we multiplied by two each term, therefore, we have a multiplication sequence. Tell students
that whenever we look for a missing number in a sequence, we inspect the numbers to discover the rule
for the sequence. Then we use the rule to find other numbers in the sequence.
- Work examples given in the book to reinforce these concepts. Tell students that sequences can be
formed out of even and odd numbers. Show examples.
- Next, present a scale of a thermometer on the board.
- Explain to students that numerical data or information many times is presented to us in the form of a
scale. Discuss what a scale is.
- With the diagram of the thermometer presented in class discuss how to find the measures being
presented here.
- Talk about the two scales (Fahrenheit scale and Celsius scale) and what is the “trick” to read the values
of each.
- Use examples given in the book to reinforce concept.
- Students work on practice set to assess their understanding of these two topics.
- Walk around to assess students work. Offer your assistance to students who might have trouble working
with the problems.
- Students exchange exercises to check work just done.

Friday:
- Students will receive Mixed Practice found on page 45 – 47 as a Test.

- Saxon Math book 7/6 pp. 30 - 47
- Rulers
- Thermometer scale
- Number line

Evaluation:

OCTUBER

Week five


Lesson Topic: Frequency Tables, Histograms, Surveys; Problems about combining and separating; place value
through trillions, multistep problems.

Class: Standard V

Previous Knowledge:

Students have worked with charts before.

Objectives:

Through class reading and discussion, and individual work, students will be able to :

Investigation 1
14. Interpret a frequency table.
15. Count and write tally marks.
16. Make a frequency table.
17. Interpret a histogram
18. Make a histogram
19. Interpret survey results.
20. Distinguish between a closed-option survey and an open-option survey.
Lesson 11
21. Identify the addition pattern in story problems about combining and separating.
22. Follow the four-step method to solve story problems about combining and separating.
23. Write an equation to solve a story problem about combining and separating.
Lesson 12
24. Identify the place value through trillions of a digit in a whole number.
25. Use words and digits to write numbers through trillions.
26. Use addition, subtraction, multiplication, and division to solve problems with several steps.

Concepts:

- Histogram - a method of displaying a range of data. A histogram is a special type of bar graph that
displays data in intervals of equal size with no space between bars.
- Survey - a method of controlling data about a particular population.
- Like stories in reading books, many of the stories we analyze in mathematics have plots. We can use
the plot of a math story to write an equation for the story. Stories with the same plot are represented
by the same equation. That is why we say there are pattern for certain plots.
- Addition pattern – some + some more = total
- Operation of arithmetic – the four basic mathematical operations: addition, subtraction,
multiplication and division.
- Place value is the value of a digit based on its position within a number.
- We use a hyphen to connect two words. Example: twenty-one, forty- five

Skills:

- Counting and marking tally marks
- Interpreting charts.
- Interpreting and making histograms and surveys.
- Follow four steps when solving story problems about combing and separating.

Attitudes:

- Respect for others and their ideas

Teaching Strategies/ Students Activities:

Day one & two:

- Have students open their books to page 48 of their books. Study the table in their books.
- Explain how we use the marks and together as a class study and interpret the information presented in
the table.
- Have students answer questions that follow in the table.
- Have a picture of a histogram on the board.
- Explain all the elements of the charts: bars, names, frequency etc…
- Relate the information that was first studied in the frequency table to the histogram.
- Have students answer the questions on page 49.
- As instructed in the book, students will be placed in groups and make a frequency table and a histogram
for the data provided.
- Have volunteers read the information on the survey and discuss.
- Study the examples provided on page 50.
- Students will answer the questions on page 51.
- Students will make a histogram based on the frequency table provided in their books.
- They will then conduct a class survey of favourite foods in the class.

Day three:

- Have a volunteer read the information in new concepts page 52.
- Analyze the problem about combining found in the book.
- Go over the steps that students need to follow to solve the problems.
- Go over each step to solve the problems provided in the book.
- Tell students to show all the steps and to write neatly. Let them know that step 4 is important because it
reminds them to reread the original problem to be sure their solution answers the question asked.
- Challenge students to write their own story problems. Have each student write one story problem about
combining or about separation.
- Ask volunteers to read the problems, and have all students write an equation for each problem.
- Students will work on practice set. Teacher will walk around checking students work and aiding those
who need help.
- Once students are done with the practice set, they will then start working on mixed practice 1 - 30.

Day four:

- Students perform warm-up activities – Multiplication facts.
- Present place value chart through trillions.
- Discuss how the place value chart works.
- Present examples of numbers through trillions and let students using the place valued chart identify the
value of different numbers.
- Remind students that commas are used after every three digits, that is after thousands, millions, billions
and trillions.
- Present different examples of numbers without the comma and let students insert commas in the
appropriate places.
- Use an example and discuss with class the correct way of writing this numbers using words.
- Have children practice writing numbers using digits as well as words.
- Provide students with multi-step problems and discuss how to go about working them.
- Present chart with terms and let students use them appropriately when solving out word problems.
- Have students work on the practice section and the problem set to assess learning.

Friday:
- Students will receive Mixed Practice found on page 61 – 62 as a quiz.

- Saxon Math 7/6 Teacher Resource Book – page 48 - 61
- Saxon Math 7/6 - Students Book – Investigation 1 and Lesson 11 - 12
- Markers
- News print
- ruler
- charts - histogram, frequency table, place value

Evaluation:

Week 6


Topics: Place Value through Trillions, Multistep Problems; Problems about Comparing, Elapsed-Time
Problems; The Number Line, Negative Numbers.

Previous Knowledge:

Students are able to read and write numbers up to million, and have been introduced to a number line in lesson
9.

Objectives:

Through research, viewing pictures, project and class discussion students will be able to:

Lesson 12
14. Identify the place value through trillions of a digit in a whole number.
15. Use words and digits to write numbers through trillions.
16. Use addition, subtraction, multiplication, and division to solve problems with several steps.
Lesson 13
17. Identify the subtraction pattern in a story problem about comparing.
18. Write and equation to solve a story problem about comparing.
19. Identify the subtraction pattern in a elapsed-time problem.
Lesson 14
20. Use a number line to order and compare integers
21. Identify numbers that are opposites.
22. Use a number line to subtract a larger number from a smaller number.
Lesson 15

23. Identify the pattern in a story problem about equal groups.
24. Write an equation to solve a story problem about equal groups.

Concepts:

- In our number system the value of a digit depends upon its position. The value of each position is called
its place value.
- The operations of arithmetic are addition, subtraction, multiplication, and division. In this table we list
the terms for the answers we get when we perform these operations.
Sum – addition, difference – subtraction, product – multiplication, quotient – division.
- Story problems about comparing have a subtraction pattern.
Large – smaller = difference ( L – S = D)
- Story problems about elapsed time contain a subtraction pattern.
Later – earlier = difference ( L – E = D)
- In a number line the points to the right of the zero represent positive numbers. The points to the left of
the zero represent negative numbers.
- Zero is neither positive nor negative.
- Negative numbers are used in various ways. A temperature of five degrees below zero Fahrenheit may
be written as -50.

Skills:

- Reading skills as students read numbers up to the trillion place value.
- Writing skills as students write numbers in digits and words
- Comparing skills as students compare numbers.
- Analyzing skills as students analyze number line.
- Comprehension skills as students understand problem solving stories.

Attitudes:

- Cooperation as students work in groups.

Teaching/Learning Strategies:

Day One

- Students perform warm-up activities – Multiplication facts.
- Present place value chart through trillions.
- Discuss how the place value chart works.
- Present examples of numbers through trillions and let students using the place valued chart identify the
value of different numbers.
- Remind students that commas are used after every three digits, that is after thousands, millions, billions
and trillions.
- Present different examples of numbers without the comma and let students insert commas in the
appropriate places.
- Use an example and discuss with class the correct way of writing this numbers using words.
- Have children practice writing numbers using digits as well as words.
- Provide students with multi-step problems and discuss how to go about working them.
- Present chart with terms and let students use them appropriately when solving out word problems.
- Have students work on the practice section and the problem set to assess learning.

Day two:

- Students perform warm up activities – Mental Math
- Review the four-step process to solve a word problem.
- Elicit from students what comparing is and discuss how it applies to word problems.
- Provide students with problems about comparing and discuss the subtraction pattern they follow.
- Talk about the common equation we get when working with these problems which will facilitate our
answers.
- Use an example to outline the steps to follow when working these types of problems.
- Explain how to go about when working with elapsed-time problems.
- Together as a class write an equation to work out this type of problems.
- Use illustrations to explain how the equation for these types of problems works.
- Have students practice several examples outlining steps for every problem correctly.
- Let students work individually on the practice section, check around the classroom and help struggling
students.

Day three:

- Students perform warm up activities – Multiplication facts
- Present a number line on a strip of paper on the blackboard.
- Elicit from students the many uses of a number line. Listen to their responses and write them on board.
- Have them look at both negative and positive numbers. Explain that numbers on opposite sides of the
zero are known as opposite pairs.
- Talk about integers and use several examples to compare them using less or more than.
- Use the number line to show how to go about subtracting different integers.
- Have students practice using different examples.
- Allow students to work on several problems of real life where you need to apply these concepts.
- Students work on problem set for home work.

Day four:

- Have students work on multiplication facts drill.

- Grant students five minutes for them to work-out these problems
- When finished, go over answers for them to check how they did.
- Provide students with example problem about equal groups.
- As a class read the problem and have students state how they would solve the problem.
- Next, explain the procedure how we go about solving problems of equal groups.
- Have students read information in their text book as you explain each step of the problem.
- Go over each example of the text book and allow students to work out the lesson practice problems.
- Check students work for misunderstanding. Allow fast learners to help with struggling students.
- Students who finish quickly start working on the mixed practice section which will be completed as part
of their homework.

Day five:

- Students will seat a test on the last five lessons covered.


- Use of worksheets
- Test/quizzes
- Construction of number lines

Reference/Materials:

- Saxon Math 7/6 Teacher Resource Book – page 58 – 71
- Saxon Math 7/6 - Students Book – Lesson 12 – 15.
- Type sheets
- Markers
- Shop paper

Evaluation:

Week seven


Lesson Topics: Problems about Equal Groups, Rounding Whole numbers, estimating, fractions and mixed
numbers, line graphs.

Previous Knowledge:

Students are familiar with fraction and number lines; they have also worked with rounding numbers in Standard
IV.

Objectives:

Through use of charts, objects, rulers, working in groups and individually, students will be able to:

1. Identify the pattern in a story problem about equal groups.
2. Write an equation to solve a story problem about equal groups.
3. Round numbers to the nearest ten, hundred, and thousand.
4. Use rounding to help estimate the answer to a problem.
5. Use estimation skills when reading graphs.
6. Determine which fraction or mixed number is represented by a point on a number line.
7. Measure length of segments to the nearest sixteenth of an inch.
8. Make equal groups to find and average.
9. Identify a number that is halfway between two numbers by finding the average of the two
numbers.

Concepts:

- Rounding off:

Rule One. Determine what your rounding digit is and look to the right side of it. If the digit is 0, 1, 2, 3,
or 4 do not change the rounding digit. All digits that are on the right hand side of the requested rounding
digit will become 0.
Rule Two. Determine what your rounding digit is and look to the right of it. If the digit is 5, 6, 7, 8, or
9, your rounding digit rounds up by one number. All digits that are on the right hand side of the
requested rounding digit will become 0.
There are points on the number line between the integers that can be named with fractions or mixed
numbers.
A mixed number is a whole number plus a fraction. Halfway between 0 and 1 is ½.
The distance between consecutive integers on a number line may be divided into halves, thirds, fourths,
fifths, or any other number of equal divisions.
Average – the number found when the sum of two or more numbers is divided by the number of
addends in the sum, also called mean.

Skills:

- Comprehension skills as students understand concepts.
- Manipulative skills as students work with objects to solve problems.
- Multiplication skills as students solve problems.
- Rounding off skills as students round off numbers.

Attitudes:

- Awareness that we use mathematics in our daily lives.
- Ability to work with others in harmony.

Teaching Strategies / Learning Activities:

Day one: no classes

Day two: Assessment (test)

Day three:
- When finished, go over the answers to check how they performed this time.
- Through questioning elicit from students the rules for rounding numbers.
- Discuss the rules and as a class go over different examples
- Have students practice rounding whole numbers.
- Have them select tow cards from a set of index cards labelled 1 – 9. Place them side by side, face
up, have the child read the number formed by the cards, and ask him/her to round the number to
the nearest ten. Check for correct answer and repeat the procedure with other students. After
students are comfortable rounding to the nearest ten, draw three cards and ask them to round the
numbers to the nearest hundred. Then ask them to draw four cards and round to the nearest
thousand.
- Discuss with students what is estimating and what background information we need to have in
order work with problems dealing with this concept.
- Present an example and together as a class, go over the procedure for solving it.
- Provide practice for students by working on lesson practice letters a – o.

Day four:
- When finished, go over the answers to check how they performed this time.
- Begin this lesson by having students create a number line from -5 to 5 and marking and labelling
fractions and mixed numbers from -41/2 to 4 1/2.
- Explain how to find fraction points using this number line.
- Next, have student create a ruler showing marks up to sixteenths.
- Provide each students with a paper in which they will form a ruler. Have them divide it in half,
then in fourths, and so on up to sixteenths.
- Explain how we use the ruler to measure objects to one sixteenth of an inch.
- Have students examine their own ruler and identify all the marks in it.
- Allow students to work on some exercises to practice measuring with a ruler to one sixteenth of
an inch.
- Finally, students will start working on mixed practice in class and complete it for homework.

Day five:
- When finished, go over the answers to check how they performed this time Procedure:
- Preview the lesson by posing the introductory story as a problem to act out. Collect 18 books
from students and make three stacks of 8, 7, and 3 books, respectively. Ask volunteers to find

the average number of books in the three stacks by reconfiguring the stacks to make three stacks
with an equal number of books in each.
- Discuss what students do in order to solve the problem.
- Go over the information on the book by reading the information as a class.
- Emphasize to students that finding an average is a two-step process that involves „combining‟
and finding „equal groups.‟
- Have students use colour tiles from paper cut outs to illustrate example 2. Give each student
piles of 3, 7, and 8 items, and have students use the objects to illustrate each step in the example.
Have them combine the three piles into one large pile and then count each item in the large pile.
Next, ask students to divide the items into three equal groups and count the number in each
group to find the average.
- Review with students how to read a line graph before solving example 4. Place an example of
the graph on the board. Ask students how to find the value of a point on the graph. Then ask
them how to estimate values that are between intervals.
- Students will start working on the lesson practice in their books. If students are unable to
complete work they will do so for homework.

Assessment strategies:

- Class participation
- Measuring objects with ruler
- Completion of written exercises
- Quiz/tests

Reference:

- Saxon math 7/6 Teachers book lesson 16 – 18
- Saxon Math 7/8 Students Book lesson 16 - 18
Materials:
- Flash cards 1 – 9
- Tape
- Rounding off chart.
- Strips of papers for number lines
- rulers

Evaluation:

Week eight


Lesson Topics: Average, Line Graph; Factors, Prime Numbers; Greatest Common Factor (GCF)

Objectives:

through class discussion, students participation, and individual work students will be able to:

- Name all the factors of a given number.
- Identify prime numbers.
- Find the greatest common factor of two or more numbers.
- Determine which fraction or mixed number is represented by a point on a number
line.
- Measure length of segments to the nearest sixteenth of an inch.
- Make equal groups to find an average.
- Identify a number that is halfway between two numbers by finding the average of
the two numbers.
- Create fraction manipulative to solve problems involving fractions.

Concepts:

- Average – the number found when the sum of two or more numbers is divided by the number of
addends in the sum, also called mean.
- A factor is a whole number that divides another whole number without a remainder.
- A prime number is a counting number greater than 1 whose only two factors are the number 1 and itself.
- Greatest Common Factor (GCF) – the largest whole number that is a factor of two or more given
numbers.

Skills:

- Identifying factors of numbers.
- Naming the prime numbers.
- Critical thinking skills as students analyze concepts.

Attitudes:

- Appreciate mathematics in our lives as it makes daily life easier.
- Respect towards others ideas and opinions.
- Leadership as they work with a partner in order to solve the mathematical problems.


Day One:

- When finished, go over the answers to check how they performed this time Procedure:
- Preview the lesson by posing the introductory story as a problem to act out. Collect 18 books
from students and make three stacks of 8, 7, and 3 books, respectively. Ask volunteers to find
the average number of books in the three stacks by reconfiguring the stacks to make three stacks
with an equal number of books in each.
- Discuss what students do in order to solve the problem.

- Go over the information on the book by reading the information as a class.
- Emphasize to students that finding an average is a two-step process that involves „combining‟
and finding „equal groups.‟
- Have students use colour tiles from paper cut outs to illustrate example 2. Give each student
piles of 3, 7, and 8 items, and have students use the objects to illustrate each step in the example.
Have them combine the three piles into one large pile and then count each item in the large pile.
Next, ask students to divide the items into three equal groups and count the number in each
group to find the average.
- Review with students how to read a line graph before solving example 4. Place an example of
the graph on the board. Ask students how to find the value of a point on the graph. Then ask
them how to estimate values that are between intervals.
- Students will start working on the lesson practice in their books. If students are unable to
complete work they will do so for homework.
Day two:

- Write the word factor on the board. Ask students if they know what factor means or if they have
ever heard the word before.
- Give and explain the definition of factors.
- After hearing the definition of a factor have students try to give examples. Teacher will then provide
examples to students.
- With the use of construction paper cut into tiles, teacher will illustrate factors of 6, 10 and 12.
- Have students read the information on their Saxon Math book on page 95.
- Explain prime numbers to students.
- Go over a few examples on how to find prime numbers with students.
- .Students will then work on practice set, page 97.
- Teacher will go around checking students work.
- Students will then start working on mixed practice on page 98, they will complete this for
homework
Day three:

- Through questioning elicit from students the definition of greatest common factor. Explain to
student what it means.
- On the board find the GCF of 12 and 18, by using a Venn diagram with two overlapping circles. The
common factors will be placed in the overlapping section.
- Go over a few examples with students without using the Venn diagram.

- Students will work on lesson practice on page 101. Teacher will walk around checking students
work.
- Time will then be taken to go over the work as a class.
- Students will then proceed and start working on Mixed Practice which will be completed for
homework.
Day four:

- Provide students with a set of fraction manipulative, they will need scissors to cut the fractional
circles.
- Have students color code the fraction manipulative to make sorting easier.
- Have students separate the fraction manipulative by cutting out the circles and cutting apart the
fraction slices along the lines.
- Students will then open their Saxon Math book to page 104. Together as a class answer the first five
questions using the manipulative.
- Students work with a partner to aanswer questions 6 – 30.
- Teacher will go around checking and aiding students with the work.

Day five: Assessment (test)


- Using manipulatives to learn about fractions
- Quiz/tests

Reference:

Materials:
- markers
- Tape
- Strips of papers for number lines
- Rulers
- Construction paper cut into small tiles

Evaluation:

Week 9


Lesson Topics: Working with Fractions using manipulative; Divisibility, and equal groups „Stories with
fractions‟

Previous Knowledge:

Students have previously worked with fractions, and have used ratio in daily life while sharing things in groups
but do not know the proper name.

Objectives:

Through class discussion, students participation, use of manipulatives, and individual work; students will be
able to:

1. Create and use a set of fraction circle manipulatives.
2. Use fraction circles to solve problems.
3. Use divisibility test to determine whether a number is divisible by 2,3,5,9, or 10.
4. Use divisibility tests to determine if 2,3,5,9 and 10 are factors of a number.
5. Use two steps to solve equal group problems with fractions.
6. Divide objects into equal groups and count to find a fractional part of number.
7. Divide a given number into equal groups and then multiply to find a fractional part of the number.

Concepts:

- There are ways of discovering whether some numbers are factors of other numbers wihtout actually
dividing. For instance, even numbers can be divided by 2. Therefore, 2 is a factor of every even
counting number.
- Tests of divisibility can help us find the factors of a number.
- In collection of objects, the collection is divided into equal groups.
- Example: What number is 2/3 of 66?
66 / 3 = 22
2 x 22 = 44
2/3 of 66 is 44

Skills:

- Identifying skills as students identify numbers that are divisible by a given number.
- Naming skills as students name the parts of fractions.
- Critical thinking skills as students analyze concepts.
- Dividing numbers into equal groups to find fractional parts of numbers.
- Identifying skills as they identify rations and write them in fraction form.

Attitudes:

- Sportsmanship as they work with a partner in order to solve the mathematical problems.

- Appreciation for numbers and knowledge for mathematical concepts


Day One:

- Have students work on multiplication facts to 49, set A. Students will be allowed 7 minutes to work
on the 100 problems. Check work as a class to find results.
Begin Lesson:

- Provide students with a set of fraction manipulative, they will need scissors to cut the fractional
circles.
- Have students color code the fraction manipulative to make sorting easier.
- Have students separate the fraction manipulative by cutting out the circles and cutting apart the
fraction slices along the lines.
- Students will then open their Saxon Math book to page 104. Together as a class answer the first five
questions using the manipulative.
- Students work with a partner to answer questions 6 – 18.
- Teacher will go around checking and aiding students with the work.

Day two:
- Have students work on multiplication facts to 49, set B. Students will be allowed 7 minutes to work
- Students will then complete questions found in their Saxon Math page 104 – 107. They will work
with the partner that they had on the previous class.
- As class, go over the work and explaining difficulties that children had while working this set.

Day three:

- Have students work on multiplication facts to 49, set C. Students will be allowed 7 minutes to work
Begin the lesson:

- Tell students to complete the mental math in page 108, on their Saxon Math.
- Once students have completed the mental math, go over the questions and answers with them
solving it together mentally.
- Go over the divisibility box with students which they have from previous class. Point out to student
that any counting number that ends with 0 is divisible by 2, 5, and 10. Give students a simple
number, such as 40 to illustrate this.

- Have volunteers read the information on “New Concepts” section from their book.
- Have different students go over to the board and solve examples.
- Analyze the examples as a class.
- Have students complete the Practice Set. Teacher will go around checking students work.
Day four:

- Have students work on multiplication facts to 49, set D. Students will be allowed 7 minutes to
work on the 100 problems. Check work as a class to find results.
Begin the lesson:

- Have students complete the mental math.
- Allow them exchange their books with one another.
- Go over the each question and work out the answer as a class.
- Use big tiles taped on the board as manipulative kits. Model example 1 for students. Use 12 tiles
to represent the 12 musicians in the problem. Divide the tiles into three equal groups, and count
the number of tiles in two of the three groups.
- Use the same procedure to solve example two with the use of the tiles.
- Once students understand the concept, go over example 3, 4, and 5 using the multiplication
symbol.
- Students will work on thirty questions found on the mixed practice.
- They will be allowed to work with a partner.
- Teacher will walk around checking students work.
- Students will finish for homework whatever they did not finish in class.
Day five:

- Have students work on multiplication facts to 49, set E. Students will be allowed 7 minutes to
- Students will receive quiz on what they have covered throughout the week. Quiz will consist of
30 problems.


- Quiz/tests

Reference:


Materials:
- Activity Master 3-7, one copy of each master per two students
- Scissors
- Plastic bags

Evaluation:

Untis of November

Week 10


fractions‟

Previous Knowledge:

but do not know the proper name. Students have also generated a manipulative fraction kit on previous classes.

Objectives:

able to:

1. Use ratios to describe relationships between numbers.
2. Identify ratios and write them in fraction forms.
3. Use fractions manipulatives to model addition and subtraction of fraction that have common
denominators.
4. Add and subtract fractions that have common denominators.
5. Write the answers to division problems as mixed numbers.
6. Write improper fractions as mixed numbers.
7. Use manipulatives to reduce fractions.
8. Add and subtract mixed numbers by first subtracting the fraction parts and then the whole-number parts.

Concepts:

- Ratio is a comparison of two numbers by division.
- When writing ratios in fraction form, we keep the following points in mind:
o We write the terms of the ratio in the order we are asked to give them.
o We reduce ratios in the same manner as we reduce fractions.
o We leave ratios in fraction form. We do not write ratios as mixed numbers.
- When fractions that have common denominators are added or subtracted, only the numerators are
added or subtracted.
- The remainder in a division problem can be written as a fraction with the remainder as the
numerator of the fraction and the divisor as the denominator.
- Circle is a closed, curved shape in which all points on the shape are the same distance from its
center.

Skills:

- Manipulative skills as students work with fraction manipulatives.
- Critical thinking skills as students solve the problems.
- Dividing numbers into equal groups to find fractional parts of numbers.

- Identifying skills as they identify rations and write them in fraction form.
Attitudes:

- Sportsmanship as they work with a partner in order to solve the mathematical problems.
- Appreciation for numbers and knowledge for mathematical concepts


Day One: Lesson 23

- Have students work on multiplication facts to 64, set E. Students will be allowed 5 minutes to work
Begin Lesson:

- Students will complete the mental math section.
- Allow them to exchange their books with one another.
- Go over the each question and work out the answer as a class.
- Have students look at the New Concept on page 119. Have volunteers read the information.
- Ask students to share their understanding of the concept.
- Clarify students‟ understanding if there is any need or further explain the concept.
- Go over example one with students.
- Emphasize to students that ratios are not expressed as mixed numbers.
- Have students read example two and have them think of how to solve the problem. Allow them a
few minutes to try to solve the problem.
- Ask students to explain how to find the number of girls in the class.
- Ask students to find the girl-boy ratio for their class.
- For further practice, ask students to write the ratio of vowels to consonants in their first name.
- Write students‟ names on the board and have students tell you their ratios. If a name has an equal
number of vowels and consonants, express the ratio as 1/1.
- Students will work on thirty questions found on mixed practice.
- They will be allowed to work with a partner.
- Walk around to observe students at their work.
- Have students work on the mixed practice section.
- Students will complete for homework whatever they don‟t finish in class.

Day two: (lesson 24 & 25)
- Have students work on multiplication facts to 64, set F. Students will be allowed 5 minutes to work

- Students take a few minutes to do the “Warm-up” exercises. Remind them that they are to do all
working out mentally.
- Students exchange their exercise books and go over each mental math problem as a class.
- Tell students that they will use their manipulative fraction kit for this lesson.
- Write two fractional problems on the board, guide students into modeling these two problems
individually.
- Work out the problems as a class.
- Write an example on the board and have students model the problem on their own. Once they have
done so go over the working out.
- Same process will be done with four other problems.
- Write examples of division problems on the board and demonstrate to students on how to write their
answers as mixed numbers.
- Provide students with work for them to do on their own. (Practice set and Mixed Practice)

Day three:

- Have students work on multiplication facts to 64, set G. Students will be allowed 5 minutes to work
Begin the lesson:

- Students do the “warm-up” exercise and exchange their books to go over each math problem as a
class.
- Have students use their fraction kit.
- Show students how to simplify and express fractions in lowest terms using the fraction kit.
- As a class work on the different examples given in the book.
- Emphasize the different steps that students need to take to solve different problems.
- Finally students work on the practice set.

Day four:

- Have students work on multiplication facts to 64, set I. Students will be allowed 5 minutes to
Begin the lesson:

- Today students will work on different word problems that they have been having difficulties
over the past days. Teacher will show steps and remind them of key words which they need to
identify when working with these problems.
- Students will follow steps along with teacher. Then they will be allowed to worm on similar
problems and the teacher will float around to check on students and also to offer assistant to
those having difficulties.

Day five:

- Have students work on multiplication facts to 64, set H. Students will be allowed 5 minutes to
30 problems.


- Completion of several practice sets
- Quiz/tests

Reference:


Materials:
- Fraction kit

Evaluation:

Week 11


fractions‟

Previous Knowledge:

but do not know the proper name. Students have also generated a manipulative fraction kit on previous classes.

Objectives:

able to:

- Identify the circumference, diameter and radius of a circle.
- Find the diameter of a circle when the radius is known and vice-versa.
- Identify parallel lines, perpendicular lines, and oblique lines.
- Name angles using one letter, three letters, or one number.
- Identify right angles, acute angles and obtuse angles.
- Identify common multiples of two numbers.
- Multiply fractions.
- Reduce fractions by common factors
- Find the least common multiple (LCM) OF TWO NUMBERS.
- Identify reciprocals as numbers that have a product of 1 when multiplied.

Concepts:

- A circle is a closed, curved shape in which all points on the shape are the same distance from its
center.
- Circumference is the perimeter of a circle.
- Compass is a tool used to draw circles and arcs.
- Diameter is the distance across a circle through its center.
- Radius is the distance from the center of a circle to a point on the circle.
- Acute angle – an angle that is less than 90°
- Right angle – an angle that is 90° exactly
- Obtuse angle – an angle that is greater than 90° but less than 180°
- Straight angle – and angle that is 180° exactly.
- Reflex angle – an angle that is greater than 180°
- When we multiply fractions, we multiply the numerators to find the numerator of the product, and
we multiply the denominators to find the denominator of the product.
- To reduce a fraction we find a common factor that divides both the numerator and denominator
evenly. Such number is found by finding the GCF of both the numerator and denominator.
- When the multiples of two or more numbers are listed in order from least to greatest, the first
number that is a common multiple is always the least common multiple (LCM).
- Least common multiple (LCM) – The smallest whole number that is a multiple of two or more given
numbers.
- Reciprocal – two numbers whose product is 1.

Skills:

- Identifying skills as students identify the parts of a circle and different angles.
- Manipulative skills as students work with fraction manipulatives.
- Critical thinking skills as students solve the problems.

Attitudes:

- Awareness that angels are found all around us.
- Respect for others as they work in groups.
- Cooperation as they work with peers.


Day One: Lesson 27

- Have students work on multiplication facts to 81, set A. Students will be allowed 5 minutes to work
Begin Lesson:

- Students do “Warm-up” exercises. Remind them that they are to do all working out mentally.
- Together as a class check results for the “warm-up” exercise.
- Demonstrate for the class how to use a compass by drawing a circle with a radius of 3 inches.
- Model for students how to draw a dot for the center before drawing the circle in case the
compass slips.
- Have students carry out activity a, b, and c on page 139.
- Elicit from students the concept of radius and diameter.
- Have them use a ruler to draw a radius and a diameter on the circles they have constructed in
parts a, b, and c of the activity.
- To reinforce the relationship between radius and diameter, ask students to find, without
measuring, the lengths of the diameters of the circles in problems a, b, and c of the activity.
- Work on the examples as a class.
- Have students work on practice set, individually.

Day two: Lesson 28
- Have students work on multiplication facts to 81, set B. Students will be allowed 5 minutes to work

- Allow students a few minutes to do the “Warm-up” exercise. Remind them that they are to do all
working out mentally.
- Once the time is up have students exchange their exercise books and go over each mental math
problem as a class.
- Have students look around the classroom and identify different types of lines.
- Explain parallel lines, perpendicular lines and oblique lines.
- Instruct students to find examples of these lines in the class or outside.
- Have volunteers read information on the book.
- Discuss information as a class, and then allow students to give more examples.
- Work on examples provided in the book with students.

- Have students work on practice set individually.
- As part of children homework, explain to them to look for pictures where these angles occur. Let
students obtain at least five pictures of different objects around the environment and identify these
angles. Children will paste these pictures on a typing sheet and will be collected for grading.

Day three: Lesson 29

- Have students work on multiplication facts to 81, set C. Students will be allowed 5 minutes to work
Begin the lesson:

- Students do the “warm-up” exercise and exchange their books to go over each math problem as a
class.
- Present students with a picture of ½ of ½ of a circle.
- Have students look at it and then instruct them that when we are looking to the answer of such a
problem we are actually multiplying.
- Tell them that the word “of” in “1/2 of ½” means to multiply. Therefore the problems becomes:
½ x ½ = ¼. This is portrayed on the graphic representation of fraction when we draw it.
- Provide other examples for students to help them reinforce and grasp this concept.
- Next, tell them that such fractions can be reduced by dividing the numerator and denominator by
common factors.
- Show them the two ways how to reduce a fraction such as 6/12.
- Tell them that there is the long way and then there is the method where we look for the GCF of
both numbers and reduce by that factor.
- Work on another example and then let students work on the practice section.
- Walk around and check to see if students are following the right steps, if not, indicate to them
where they are going wrong.
- Use fast learners to help others understand the concepts.
- Students will work on problem set of this lesson for homework.
Day four: Lesson 30

Begin the lesson:

- Students begin the lesson by doing the “warm up” exercises.

- Remind them to work these problems mentally.
- Together as a class check answers on this section.
- Explain to students that they are going to be working on a new math skill this morning and they
already know the first steps.
- Tell that we are going to be looking for the Least common multiple (LCM)
- Provide them with the numbers 2 and 3 and ask them to look for the multiples of these two
numbers.
- Elicit answers from students and write them on the board.
- Next, ask students to circle all the common multiples found in the two numbers.
- Now have students write all the common multiples.
- Tell them to select the least multiple.
- Inform students that they have just found the LCM of 2 and 3 which is 6.
- Allow students to work on another examples and then work on the next part of the lesson.
- Present students with the term “reciprocals” and explain what it means.
- Show students the different examples of the lesson and explain how to work these examples.
- Children work the examples along with the teacher so that they can also practice as the teacher
explains.
- Work on examples with whole numbers and fractions.
- Children will then be allowed to work on the practice set of the lesson.
Day five:

30 problems.


- Quiz/tests

Reference:


Materials:
- Fraction kit
- Compass

- Typing sheets
- Bristol board
- markers

Evaluation:

Week 12 – Children’s week

Week 13 – Review Week

December

Week 14 – Exam Week

Week 15 – Exam discussion – Christmas Program – class party – closure

January

Week 16


Lesson Topics: Least Common Multiple, Reciprocals; Measuring and Drawing Angles with a Protractor;
Areas of Rectangle; Expanded Notation, More on Elapsed Time; Writing Percent as Fractions, part 1

Previous Knowledge:

Students have worked with multiples, and have studies angles

Objectives:

Through investigation, cooperative learning, individual work and use of manipulatives, students will be able to:

1. Identify common multiples of two numbers.
2. Find the least common multiple (LCM) OF TWO NUMBERS.
3. Identify reciprocals as numbers that have a product of 1 when multiplied
4. Use a protractor to find the measure of an angle and to draw an angle with the given
measurement.
5. Identify square units as the units used to measure area.
6. Multiply length by width to find the area of a rectangle.
7. Find the side length and the perimeter of a square when the area of the square is known.
8. Write a number in expanded notation,
9. Rename hours and minutes as minutes to solve an elapsed-time problem.
10. Write percent as a reduced fraction.

Concepts:

- When the multiples of two or more numbers are listed in order from least to greatest, the first
number that is a common multiple is always the least common multiple (LCM).
- Least common multiple (LCM) – The smallest whole number that is a multiple of two or more given
numbers.
- Reciprocal – two numbers whose product is 1.
- Protractor – is a tool used to measure and draw angles.
- To ensure that the correct scale on the protractor is used, it helps to decide whether an angle is acute,
obtuse, or right before measuring.
- Area is the number of square units needed to cover a surface.
- Formula for finding area of a rectangle = Length x Width
- To write a number in expanded notation, each nonzero digit is written times its place value.
Example: (3 x 1000) + (9 x 100) + (4 x 10)
- The hours of the day are divided into two parts: a.m. and p.m. We can use the later-earlier difference
pattern to solve elapsed-time problems about hours and minutes.
- A percent is actually a fraction with a denominator of 100. The word percent and its symbol %,
mean “per hundred.” To write a percent, we remove the percent sign and write the number as the
numerator and 100 as the denominator.

Skills:

- Identifying skills as students identify common multiples of two numbers.
- Use of a protractor to measure and draw angles.
- Calculating area of a rectangle in square units by multiplying length multiplied by width.
- Reducing fractions.

Attitudes:

- Cooperation as they participate in class and pair activity.
- Awareness of new concepts learnt in lessons.
- Confidence in math.


Day 1: Lesson 30

- Have students work on multiplication facts to 121, set A. Students will be allowed 5 minutes to
Begin the lesson:

- Explain to students that they are going to be working on a new math skill this morning and they
already know the first steps.
- Tell that we are going to be looking for the Least common multiple (LCM)
- Provide them with the numbers 2 and 3 and ask them to look for the multiples of these two
numbers.
- Elicit answers from students and write them on the board.
- Next, ask students to circle all the common multiples found in the two numbers.
- Now have students write all the common multiples.
- Tell them to select the least multiple.
- Inform students that they have just found the LCM of 2 and 3 which is 6.
- Allow students to work on another examples and then work on the next part of the lesson.
- Present students with the term “reciprocals” and explain what it means.
- Show students the different examples of the lesson and explain how to work these examples.
- Children work the examples along with the teacher so that they can also practice as the teacher
explains.
- Work on examples with whole numbers and fractions.

- Children will then be allowed to work on the practice set of the lesson.
Day 2 :( Investigation 3)

- Have students work on multiplication facts to 121, set B. Students will be allowed 5 minutes to
- Begin lesson by showing students a protractor.
- Elicit from students the use of this instrument.
- Read information about it found in their math books and discuss it with them.
- Use an enlarge version of a protractor to draw several types of angles on the board to
demonstrate how to use it.
- Have students carry out the activity on their books and guide them how to successfully complete
it.
- Draw some more examples for them, clearly showing how to use the protractor to draw angles.
- Tell students to work on the practice section.
- Move around checking students work and the proper use of the protractor.
Day 3 (lesson 31)

- Have students work on multiplication facts to 121, set C. Students will be allowed 5 minutes to
- Have students use their math books and measure the length and width of their books.
- Have them add up the measurements.
- Elicit from students what measurements they have calculated – perimeter.
- Have students multiply these two measures.
- Inform them that they have calculated area.
- Together as a class read concepts in the book and discuss each one.
- Go over and explain the different examples in the book.
- Then have students work on the practice section for this lesson.
- Go around identifying possible problems and helping those children that are having difficulties.
- Students begin the mixed practice in class and finish it for homework.

Day 4: Lesson 32

Expanded Notation

- Allow volunteers from the class to read information on New Concepts found in their books.
- Provide examples on expanded notation to students and show them how to go about do it.
- Go over examples given in the book.

Elapsed Time:

- Review the concepts of a.m. and p.m. with the class.
- Discuss what elapsed time means.
- Work on different examples from the books to teach this concept.
- Make sure students follow step by step each example given as this type of problems usually creates
confusion.
- At the end have students work on the practice section of both parts of the lesson taught today.
- Go over any misconceptions that students might have.

Day 5 (lesson 33)

- Students perform the “Warm Up” exercises.
- Remind them to work on each problem mentally.
- Have them exchange exercises and check the work as a class.
- Have volunteer read the information on New Concept in their books
- Explain examples found in the book.
- Have students work on some to assess understanding.
- Then let them work on the practice section individually.
- Students who finish first will help the teacher check and help other struggling students.
- Once students are finished they will begin working on the mixed practice which will be finished
as part of their homework.


- Written exercises

- Test/quizzes

Reference:

- Saxon Math 7/6 Teachers Resource Book. Lessons 30 to 33
- Saxon Math 7/6 Students Book. Lessons 30 to 33

Materials:
- Protractor
- Place value chart
- Compass
- Rulers

Evaluation:

Week 17


Lesson Topics: Writing Percent as Fractions, part 1; Decimal Place Value; Writing decimal numbers as
fractions; Reading and writing decimal numbers; Subtracting Fractions and Mixed Numbers from Whole
Numbers

Previous Knowledge:

Students know that percentage is out of a 100, they also have a good knowledge of whole number place values,
as well of fractions and mixed numbers.

Objectives:

Through discussion, cooperative learning, individual work and use of illustrations, students will be able to:

11. Write percent as a reduced fraction.
12. Identify the value of the decimal places through millionths.
13. Write a decimal number as a fraction.
14. Read and write a decimal number.
15. Subtract a mixed number from a whole number.
16. Convert a whole number into a fraction name for one.

Concepts:

- A percent is actually a fraction with a denominator of 100. The word percent and its symbol %,
mean “per hundred.” To write a percent, we remove the percent sign and write the number as the
numerator and 100 as the denominator.
- Each place to the right of the ones place has a value that is one tenth of the value of the place to its
left.
- Decimal numbers are actually fractions of denominators 10, 100, 1000 and so on. The denominator
of decimal is not written. Instead, the denominator is indicated by the number of decimal place
values.
- To subtract a mixed number from a whole number we first change the whole number into a whole
number plus a fraction name for one (e.g. 5 is change into 4 plus 3/3). It depends on the denominator
of the fraction of the mixed number.
Skills:

- Writing and reading decimals
- Subtracting mixed numbers from whole numbers
- Reducing fractions.
Attitudes:



Day 1 (lesson 33)

- Have volunteer read the information on New Concept in their books
- Explain examples found in the book.
- Have students work on some to assess understanding.
- Then let them work on the practice section individually.
- Students who finish first will help the teacher check and help other struggling students.
- Once students are finished they will begin working on the mixed practice which will be finished
as part of their homework.
Day 2 :( Lesson 34)

- Have students work on multiplication facts to 121, set F. Students will be allowed 5 minutes to
- Students work on the “Warm Up” exercises.

- As a class go over the work.
- Use illustrations and discuss the new concept with students.
- Place a decimal chart on the board and go over the examples given on the book with students.
- Involve students while explaining examples to come to the board and help solve the examples
given.
- As practice and assessment, have students work on practice set a – d.

Day 3 (lesson 35)

- Have students work on multiplication facts to 121, set G. Students will be allowed 5 minutes to
- Students work on the “Warm Up” exercises.
- As a class go over the work.
- Have students go to page 183. Discuss with students how to write fractions from decimal
numbers.
- Explain to students that one decimal place value after the decimal place has a denominator of 10,
then 100, 1000 and so on.
- Have students notice that the number of zeros in the denominator equals the number of decimal
places in the decimal number. Example: 0.003 = 3/1000
- Tell students that the digits to the right of the decimal point are written as the numerator of the
fraction. Explain that when one or more zeros come directly after the decimal point but before a
nonzero digit, the zeros are not written in the numerator.
- Write different decimal numbers on the board. Have students practice reading decimal numbers
aloud.
- Go over the examples provided on the book.
- Have students work on lesson practice from lesson 35
- Go around checking students work and helping those who might have any misunderstanding.
Day 4: assessment

- Students will do the mixed practice of lesson 35 as part of their weekly evaluation (test)
- Note that one of the groups will do it the next day (day 5)

Day 5: lesson 36

- Have students work on multiplication facts to 121, set H. Students will be allowed 5 minutes to
- Students work on the “Warm Up” section.

- Go over the work once there are finished.
- Present topic to students and tell that today they will learn how to subtract mixed numbers from
whole numbers.
- Read a “separating” story problem about pies.
- Show illustrations of this story to students for better understanding.
- Discuss with class the step taken to solve this type of problems.
- Have students clearly understand how to change whole number into fraction name for one as this
skill is important to subtract mixed numbers form whole numbers.
- Work several examples along with the class by eliciting the various steps from students.
- Have students work on the practice set.
- Provide extra practice for students who are struggling.
- Give them one to one instructions and involve their classmates to help them understand how to
solve these problems.

- Written exercises
- Test/quizzes

Reference:

- Saxon Math 7/6 Teachers Resource Book. Lessons 33 to 36
- Saxon Math 7/6 Students Book. Lessons 33 to 36

Materials:
- Bristol Board
- Place value chart
- Ruler

Evaluation:

Week 18


Lesson Topics: Adding and Subtracting Decimal numbers; Adding and Subtracting Decimal Numbers and
Whole Numbers; Squares and Square Roots; Multiplying Decimal Numbers; Using Zero as a Placeholder;
Circle Graphs

Previous Knowledge:

Students are aware of decimal numbers and can read and write them.

Objectives:

Through discussion, cooperative learning, individual work and use of illustrations, students will be able to:

17. Add and subtract decimal numbers.
18. Write a whole number with a decimal point.
19. Add decimal numbers and whole number.
20. Subtract decimal numbers from a decimal numbers.
21. Square a number.
22. Use the exponent 2 to indicate squaring or square units.
23. Simplify and expression by applying exponents and then adding, subtracting, multiplying, or
dividing.
24. Find the square root of a number
25. Multiply a decimal number by a decimal number.
26. Multiply a decimal number by a whole number.
27. Use zeros to fill in each empty decimal place when subtracting, multiplying, and dividing
decimal numbers.
28. Use zeros as placeholders as needed when writing in digits the word form of a decimal number.
29. Interpret information displayed in a circle graph.

Concepts:

- We line up decimal numbers for addition and subtraction by lining up decimal points.
- To find the sum of a decimal number and a whole number, write the whole number with a decimal
point and line up the decimal points before adding.
- Squares and square roots – from the model of a square comes the expression “squaring number.” We
square a number by multiplying the number by itself. “Five squared” is 5 x 5, which is 25. To
indicate squaring, we use the exponent 2. 52 = 25. “Five squared equals 25.” Notice that the
exponent is elevated and written to the right of the 5. An exponent shows how many times the other
number, the base, is to be used as a factor. In this case, 5 is to be used as a factor twice.
- A number is a perfect square if it has a square root that is a whole number. Starting with 1, the first
four perfect squares are 1, 4, 9, and 16.
- The number of decimal places in the product is determined by counting the total number of decimal
places in the factors.
- When subtracting, multiplying, and dividing decimal numbers, we often encounter empty decimal
places. When this occurs, we will fill each empty decimal place with a zero. In order to subtract, it is
sometimes necessary to attach zeros to the top of the number.
- Circles graphs, which are sometimes called pie graphs or pie charts, display quantitative information
in fractions of a circle.

Skills:

- Adding whole and decimal numbers
- Multiplying decimal numbers
- Finding the square roots of numbers
Attitudes:



Day 1 (lesson 37)

- Have students work on multiplication facts to 144, set A. Students will be allowed 5 minutes to
- Students work on the “warm up” section.
- Go over the work together as a class once they are finished.
- Present two problems of addition and subtraction of decimal numbers to students.
- Have students try to find a solution to solve the problems.
- Invite a student who has come up with the solution to the problems to come to the board and
show the class.
- If nobody can come up with a solution, show students how to work out this type of problems.
- Remind students of the important rule to follow when adding and subtracting decimal numbers.
- Go over the examples given in the books with students.
- Finally have them work on the practice section and check their work to assess for understanding
of the concepts.

Day 2 (lesson 38)

- Have students work on multiplication facts to 144, set B. Students will be allowed 5 minutes to
- Show students how to write dollars in two ways.
- Write any number and show students how to write in four different ways, with decimal and
without decimal numbers

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