EXPLICIT INSTRUCTION
Explicit Instruction: Lesson Planning
Group being taught: 8th graders in beginning algebra class
Prior instruction: The students have been introduced to the concepts of variable and expression and how to evaluate a simple expression. Goal of the lesson: The students will learn the first step in the order of operations: solve the operations in the parentheses first.
Larger goal: Students will learn all components in the order of operations: 1) parentheses, 2) exponents, 3) multiplication/division left to right, 4) addition/subtraction left to right. They will learn a mnemonic device to help them remember the order of operations: 1) Please, 2) Excuse, 3) My Dear, 4) Aunt Sally.
Opening of Lesson
Gain Students Attention. Students, please put all of your materials away except your math log, a pencil, and your math book. (The teacher pauses.) Look up here.
State the goal of the lesson and its relevance. Today we are going to continue our work with variables and expressions. You are going to learn how parentheses are used in expressions. This knowledge is critical in solving algebraic equations.
Review Critical Prerequisite skills. But first, let’s do a little review. Ones, tell your partner what a variable is? (The teacher monitors and calls on a student.) A variable is a symbol that represents a number. Yes, a variable is a symbol that represents a number. Look at these expressions (3 + x; t – 6). In the first expression, what is the variable? Everyone. X. Yes, x is a symbol that represents a number. Everyone, what is the variable in the second expression? T. Correct. Let’s look again at the definition of an expression. (The teacher displays the definition on the overhead.)
expression
• mathematical statement
• that may use o numbers
o variables or
o both
(The teacher displays the following items on the overhead.)
1. 2
2. x
3. #
4. 2 + 6 – y
5. *
Check each of these items against the definition.
On your paper, write the items that are expressions (Teacher monitors and then asks individuals the following questions.) Why is 2 an expression? It is a number. Why is x an expression? X is a variable. Why is the heart not an expression? It is not a mathematical statement. It is not a number or a variable representing a number. Why is 2 + 6 – y an expression? It contains both a number and a variable. Why is the square not an expression? It is not a mathematical statement. Also, it is neither a number nor a variable. WOW… you really have mastered these concepts. Let’s learn more about expressions.
Body of Lesson
Phase ONE: Instruction models and explain strategies
Modeling (I do it.)
(The teacher writes 5 × (6 + 3) on the overhead transparency.) Look at this expression. When an expression contains more than one
operation, parentheses can be used to show which computation should be done first. So when we have an expression, we first look for parentheses and do the operation or operations inside the parentheses. In this problem, 6 + 3 is inside the parentheses, so I will do that operation first. What is 6 + 3, everyone? 9. (The teacher writes 9 below 6 + 3.) After I have done the operation inside the parentheses, I can do the remaining operation. Everyone, what is 5 × 9? 45. The value of this expression is 45.
Look at this expression.
(Teacher writes (5 × 6) + 3). Notice that it has the same numbers and operations as the previous problem. However, the parentheses are in a different location. First, we do the operations inside the parentheses. What is 5 × 6, everyone? 30. (Teacher writes 30 below 5 × 6.) Now, I can do the remaining operation. What is 30 + 3? 33. Notice that the expression has a different value when the parentheses are in a different location. (Teacher writes 63 − (4 − 3) on the board.) Help me do this problem. Should I do the operations inside or outside of the parentheses first? Inside. What is 4 − 3? 1. (The teacher writes 1 under 4 − 3.) Now, I can do the remaining operation. What is 63 − 1? 62.
PHASE Two: Practice Opportunities
Prompted/Guided Practice (We do it.)
Let’s do some problems together. Please stay with me so we can do these items correctly. (Teacher writes (63 − 4) − 3 on the transparency.) Write this expression on your paper, but don’t solve it. Do we do the operations inside or outside of the parentheses first? Inside. Write the answer to 63 − 4 on your paper. Put your pencil down to show that we can go ahead. (The teacher writes 59 below 63 − 4). Check your answer. Now, do the remaining operation. (Teacher monitors and writes 56.) So, the value of this expression is 56. Notice that the expression has a different value than the previous expression when the parentheses were in a different location
(Teacher writes 15 − (9 + 6) on the transparency). Write this expression on your paper. Put your pencil down when you are done. Do we do the operations inside or outside of the parentheses first? Inside. Good, find the value of this expression. (Teacher moves around the room and monitors students. Then, the teacher writes the completed item on the transparency and has students check their work.)
(Teacher writes (15 – 9) + 6) on the transparency.) Write this expression on your paper. Do we do the operations inside or outside of the parentheses first? Inside. Find the value of the expression. (Teacher monitors and provides feedback.) Look at these two expressions. They had the same numbers and operations but different values. You can see how important it is to do the operations within the parentheses first.
(Teacher writes (35 − 5) − (4 + 2) on the transparency.) Copy this expression. Do we do the operations inside or outside of the parentheses first? Inside. Yes, here you have two sets of parentheses. Do the operations inside both sets of parentheses and then subtract. Find the value of the expression. (Teacher monitors and provides feedback.)
(Teacher writes (9 + 16) − (16 − 8) on the transparency.) Copy this expression and find the value of the expression. Don’t forget . . . parentheses first. (Teacher monitors and provides feedback.) Terrific.
Unprompted Practice (You do it.)
Find the value of item #A. Put your pencil down when you are done. (Teacher monitors and then provides feedback on the item. This is repeated for #B.) Now, complete the remaining problems and then we will go over them. (Teacher monitors and then provides feedback to the group.) A. (6 × 5) − 4 B. 6 × (5 − 4) C. (5 + 6) × (8 − 2) D. (13 − 3) × (10 − 5) E. (9 × 2) − 8
Closing of the Lesson Review. Today you learned the first step in an algebra strategy called the Order of Operations. First, we do the operations that are inside the __________. Parentheses. Yes, we always do the operations inside the parentheses before those outside of the parentheses.
Preview. Tomorrow, we will learn about the second operation in the order of operations: exponents.
Assessment
Independent Work.
Please open your Algebra book to page 5. Complete the items in Set A. We will check your homework at the beginning of class tomorrow.
Group being taught: 8th graders in beginning algebra class
Prior instruction: The students have been introduced to the concepts of variable and expression and how to evaluate a simple expression. Goal of the lesson: The students will learn the first step in the order of operations: solve the operations in the parentheses first.
Larger goal: Students will learn all components in the order of operations: 1) parentheses, 2) exponents, 3) multiplication/division left to right, 4) addition/subtraction left to right. They will learn a mnemonic device to help them remember the order of operations: 1) Please, 2) Excuse, 3) My Dear, 4) Aunt Sally.
Opening of Lesson
Gain Students Attention. Students, please put all of your materials away except your math log, a pencil, and your math book. (The teacher pauses.) Look up here.
State the goal of the lesson and its relevance. Today we are going to continue our work with variables and expressions. You are going to learn how parentheses are used in expressions. This knowledge is critical in solving algebraic equations.
Review Critical Prerequisite skills. But first, let’s do a little review. Ones, tell your partner what a variable is? (The teacher monitors and calls on a student.) A variable is a symbol that represents a number. Yes, a variable is a symbol that represents a number. Look at these expressions (3 + x; t – 6). In the first expression, what is the variable? Everyone. X. Yes, x is a symbol that represents a number. Everyone, what is the variable in the second expression? T. Correct. Let’s look again at the definition of an expression. (The teacher displays the definition on the overhead.)
expression
• mathematical statement
• that may use o numbers
o variables or
o both
(The teacher displays the following items on the overhead.)
1. 2
2. x
3. #
4. 2 + 6 – y
5. *
Check each of these items against the definition.
On your paper, write the items that are expressions (Teacher monitors and then asks individuals the following questions.) Why is 2 an expression? It is a number. Why is x an expression? X is a variable. Why is the heart not an expression? It is not a mathematical statement. It is not a number or a variable representing a number. Why is 2 + 6 – y an expression? It contains both a number and a variable. Why is the square not an expression? It is not a mathematical statement. Also, it is neither a number nor a variable. WOW… you really have mastered these concepts. Let’s learn more about expressions.
Body of Lesson
Phase ONE: Instruction models and explain strategies
Modeling (I do it.)
(The teacher writes 5 × (6 + 3) on the overhead transparency.) Look at this expression. When an expression contains more than one
operation, parentheses can be used to show which computation should be done first. So when we have an expression, we first look for parentheses and do the operation or operations inside the parentheses. In this problem, 6 + 3 is inside the parentheses, so I will do that operation first. What is 6 + 3, everyone? 9. (The teacher writes 9 below 6 + 3.) After I have done the operation inside the parentheses, I can do the remaining operation. Everyone, what is 5 × 9? 45. The value of this expression is 45.
Look at this expression.
(Teacher writes (5 × 6) + 3). Notice that it has the same numbers and operations as the previous problem. However, the parentheses are in a different location. First, we do the operations inside the parentheses. What is 5 × 6, everyone? 30. (Teacher writes 30 below 5 × 6.) Now, I can do the remaining operation. What is 30 + 3? 33. Notice that the expression has a different value when the parentheses are in a different location. (Teacher writes 63 − (4 − 3) on the board.) Help me do this problem. Should I do the operations inside or outside of the parentheses first? Inside. What is 4 − 3? 1. (The teacher writes 1 under 4 − 3.) Now, I can do the remaining operation. What is 63 − 1? 62.
PHASE Two: Practice Opportunities
Prompted/Guided Practice (We do it.)
Let’s do some problems together. Please stay with me so we can do these items correctly. (Teacher writes (63 − 4) − 3 on the transparency.) Write this expression on your paper, but don’t solve it. Do we do the operations inside or outside of the parentheses first? Inside. Write the answer to 63 − 4 on your paper. Put your pencil down to show that we can go ahead. (The teacher writes 59 below 63 − 4). Check your answer. Now, do the remaining operation. (Teacher monitors and writes 56.) So, the value of this expression is 56. Notice that the expression has a different value than the previous expression when the parentheses were in a different location
(Teacher writes 15 − (9 + 6) on the transparency). Write this expression on your paper. Put your pencil down when you are done. Do we do the operations inside or outside of the parentheses first? Inside. Good, find the value of this expression. (Teacher moves around the room and monitors students. Then, the teacher writes the completed item on the transparency and has students check their work.)
(Teacher writes (15 – 9) + 6) on the transparency.) Write this expression on your paper. Do we do the operations inside or outside of the parentheses first? Inside. Find the value of the expression. (Teacher monitors and provides feedback.) Look at these two expressions. They had the same numbers and operations but different values. You can see how important it is to do the operations within the parentheses first.
(Teacher writes (35 − 5) − (4 + 2) on the transparency.) Copy this expression. Do we do the operations inside or outside of the parentheses first? Inside. Yes, here you have two sets of parentheses. Do the operations inside both sets of parentheses and then subtract. Find the value of the expression. (Teacher monitors and provides feedback.)
(Teacher writes (9 + 16) − (16 − 8) on the transparency.) Copy this expression and find the value of the expression. Don’t forget . . . parentheses first. (Teacher monitors and provides feedback.) Terrific.
Unprompted Practice (You do it.)
Find the value of item #A. Put your pencil down when you are done. (Teacher monitors and then provides feedback on the item. This is repeated for #B.) Now, complete the remaining problems and then we will go over them. (Teacher monitors and then provides feedback to the group.) A. (6 × 5) − 4 B. 6 × (5 − 4) C. (5 + 6) × (8 − 2) D. (13 − 3) × (10 − 5) E. (9 × 2) − 8
Closing of the Lesson Review. Today you learned the first step in an algebra strategy called the Order of Operations. First, we do the operations that are inside the __________. Parentheses. Yes, we always do the operations inside the parentheses before those outside of the parentheses.
Preview. Tomorrow, we will learn about the second operation in the order of operations: exponents.
Assessment
Independent Work.
Please open your Algebra book to page 5. Complete the items in Set A. We will check your homework at the beginning of class tomorrow.