Solving Multi-Step Math Problems, Questionnaire Example

Sequence of Instructional Procedures/Activities/Events (provide description and indicate approximate time for each):

 Identification of Student Prerequisite Skills Needed for Lesson:

To cultivate the learners’ interest, I will engage them in a short “mind-reading” game, whereby I’ll ask one student to think of a number, and keep it secret. I will tell him/her to add another number, say 20, to the number he/she thought of, and ask for the answer. Depending on the answer given, say 45, I will reveal the “secret” number to be 25 by subtracting 20 from the sum. Then I’ll challenge the class to explain how I was able to find out the original number.

Presentation of New Information or Modeling:

I will demonstrate by explaining that I assumed y to be the number. To determine y, I subtracted 20 from 45, because 45 is the sum of y and 20. I’ll write an equation to represent the operation: y + 20 = 45; which number, when added to 20 gives you 45? The answer is subtracting 20 from 45. Therefore; y= 45- 20, = 25.

I’ll explain to students that since 3^rd grade they have been learning how to add and subtract 2 and 3 digit values. However, they were provided with complete problems to solve. In this unit, they will learn how to formulate the problems using given information and then solving the problems (5 min).

2.1 I will explain to learners the meaning of a mathematical expression/equation; a formulation using numbers and symbols to represent a mathematical problem. For instance, y + 20 is an expression. When we introduce the “=” sign to express its total value, i.e. what it equals to, it becomes an equation, thus: y + 20 is an expression, and y+ 20 = 45 is an equation.

2.1. I will use examples to show the pupils how to form mathematical expressions and equations from word problems, and how to solve them.

Example 1.1:

Sam was given x$ by his father to spend during his birth day. By the end of the day, he realized that he had only 50$ remaining. Formulate an expression to show how much money Sam had spent.

Ans. The total amount Sam had was x, and remained with $50 after spending. Therefore, the amount Sam spent is x- 50.

Example 1.2:

If Sam spent $150, how much was he given?

Original amount = x

Amount spent= 150

Amount remaining= 50

Therefore, x= amount spent plus amount remaining; = 150+ 50; x= 200 (10 min).

2.2. I will ask students to identify the correct expressions from the given word problems.

Example 2.2.1:

Sandy’s family had y hens, and 38 of them died from avian flu. Which expression shows the number of hens remaining?

1. 38+ y
2. y- 38
3. 38-y.

If the remaining number of hens was 25, which equation shows the number of hens Sandy’s family had originally?

1. y= 38- 25
2. y= 25- 38
3. y= 25= 38 (5 min).

Independent Student Practice:

I will give a word problem and ask each student to formulate expressions and equations on their work sheets, and solve the equations.

3.1: There are n students in a class, and 48 are boys.

1. formulate an expression to show the number of girls in the class
2. if there are 33 girls, formulate and solve an equation for the total number of students in the class.

Culminating or Closing Procedure/Activity/Event:

 I will walk around the class and mark each student’s work, and correct those who have problems following.

Pedagogical Strategy (or Strategies):

I will ask one student who got all the steps correct to work out the problem on the board for the others to follow.

Differentiated Instruction:

During classroom assessment (while marking the students’ work) I will spend more time those students with learning disabilities and ESL students, and give them an additional word problem to work out. I will mark their work and make necessary corrections (15 min).

Student Assessment/Rubrics:

I will give a practice exercise of 6 word problems, which the students will work out individually by formulating mathematical expressions and equations, and then solving the. Mastery of the lesson will be determined if students get 5/6 and above of the problems correct. I will plan for extra teaching for those who get less than 5 of the problems wrong.

Practice Exercise:

John spent $y on his shopping, and remained with $357.

• Form an expression to show the amount John spent on shopping
• If John had spent $546, form an equation to show the total amount he had, and find out the value of y.

There were 375 guests invited to a party, and only x guests attended.

• Form an expression to show the number of guests who did not attend the party.
• If 309 guests attended the party, how many failed to attend?

A shopkeeper weighed out y kilograms of sugar from a sack of 100 kilograms.

• Form an expression to show the quantity of sugar in kilograms that remained in the sack.
• Later on, the shopkeeper’s wife took 5 kilograms from the sack and took it home, and when he weighed the remaining sugar, he had 33 kilograms. How many kilograms of sugar did the shopkeeper weigh out of the sack initially?

50 students were registered for an exam, and x of them were sick during the exam day.

• Form an expression to show the number of students who sat for the exam.
• Sam noted that only 37 desks were occupied during the exam. Find the value of x.

There are 3657 teachers in Wisconsin state. N teachers will retire by the end of the year.

• By way of a mathematical expression, show the number of teachers who will still be teaching next year.
• 3509 teachers reported for the New Year. Form an equation to show the number of teachers who retired. Find the value of n.

Becky did seven subjects, and scored a total of 596 points. She scored y points in English, History and Geography.

• Form an expression to show the number of points she scored English, History and Geography.
• When Becky added her score in the remaining subjects, she realized that she had scored 20 more points than her classmate’s 350 in the same subjects. How many points did Becky score in English, History, and Geography? (35 min).