basic math presentation - building a model

8/2/2019 Basic Math Presentation - Building a Model

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BY: JASLYN EMA AK MENIKLEE ZHAO HUI

Problem Solving Strategy

Building A Model1


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Building A Model

Mathematics is a way of modelling the real world. A mathematicalmodel has traditionally been a form of an equation.

The use of physical models is often useful in solving problems.

There may be several models appropriate for a given problem. Thechoice of a particular model is often related to the students previousknowledge and problem-solving experience.

Objects and drawings and writing an equation are also abstract

ways of modelling a problem situation. The use of modellingprovides a method for organizing information that could lead to theselection of another problem-solving strategy.

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Building A Model

Types of models

Mathematics modeling

Discrete model

Continuous model

Probabilistic model

Waves & oscillations model Optimization model

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Building A Model - Physical Models

Question 1:

Four holes are drilled in a straight line in a rectangular

steel plate. The distance between hole 1 and hole 4 is 35

cm. The distance between hole 2 and hole 3 is twice the

distance between hole 1 and hole 2. The distance

between hole 3 and hole 4 is the same as the distance

between hole 2 and hole 3. What is the distance, in

centimetres, between the centre of hole 1 and the centre

of hole 3?

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UNDERSTAND THE PROBLEM:

We want to know the distance between hole 1 and hole 3.

1. What is the distance from hole 1 to hole 4?

35 cm2. What is the distance from hole 1 to hole 2?

Half the distance from hole 2 to hole 3

3. What is the distance from hole 3 to hole 4?

The same as from hole 2 to hole 3

DEVISE A PLAN:

Building A Model Physical Models

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CARRYING THE PLAN :

Mark off a distance of 35 cm on a rectangular steel plate.

Place a marker labelled 1 at the zero point and one labelled 4 atthe 35-cm point.

Place markers 2 and 3 between 1 and 4.1) Move 2 and 3 until the distances between 2 & 3 and 3 & 4 are

equal.

2) Distance between 1 & 2 =half the distance between 2 & 3

Adjust the markers until both of these conditions are met. Measure the distances to double check.

The distance between 1 and 3 is 21 cm.

21cm

0 35RectangularSteel Plate

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LOOK BACK :

Does our answer seem reasonable?

Yes, the answer must be less than 35cm.

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Building A Model - Drawings or Sketches

Question 2:

If an eight-inch-square cake serves four people,

how many 12-inch-square cakes are needed to

provide equivalent servings to 18 people?

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UNDERSTAND THE PROBLEM :

We need to find out how many 12 12 cakes areneeded. From the question, we know that:

1. How big is the original cake? 8 8

2. How many people did it feed? 4

3. How big are the other cakes? 12 124. How many people must they feed? 18

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DEVISE A PLAN :

How should we approach this problem?

Diagram the cakes to understand the size of the portions.

CARRYING THE PLAN :

Draw an 8 8 cake and cut it into 4 equal pieces. Sinceeach piece is a square with side length of 4, the area of

each piece is 4 4 = 16 square inches.

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4

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So each person gets 16 square inches of cake.

18 people times 16 square inches per person equals 288total square inches of cake needed.

We know that a 12 12 cake contains 144 square inchesof cake.

288 divided by 144 equals 2, so two 12 12 cakes arerequired to feed 18 people.

LOOK BACK :

Did we answer the correct question, and does our answerseem reasonable? Yes.

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Building A Model - Use Equations

Question 3:

Linda has a total of RM72.00, consisting of an equal

number of 1 cent, 5 cents, 10 cents and 20 cents.

How many coins does she have in all?

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UNDERSTAND THE PROBLEM :

We want to know how many coins Linda has.

How much money does she have total? RM72.00

How many of each coin does she have?We dont know exactly, but we know that she has an

equal number of each coin.

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DEVISE A PLAN :

We know how much each coin is worth, and we

know how much all of her coins are worth total, so

we can write an equation that models the situation.

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CARRYING THE PLAN:

Let p = the number of 1 cent

n = number of 5 cents

d = number of 10 centsq = number of 20 cents

From the equation above,

Equation: p + 5n + 10d + 20q = 7200

We know that she has an equal number of each coin, so p =n = d = q.

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Substitute p into the equation,

p + 5p + 10p + 20p = 7200

36p = 7200

p = 200

Linda has 200 one cent. Since she has an equal

number of each coin, she also has 200 five cents,200 ten cents and 200 twenty cents.

Therefore, she has 800 coins.

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LOOK BACK :

Did we answer the question asked?

Yes. Does our answer seem reasonable?

Yes, we know the answer must be less than 7200

(for the number of coins if they were all 1 cent andgreater than 360 (the number of coins if they were all20 cents).

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Reference List

http://www.spring-

ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheet

s/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem

%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexago

n%20Problem%20Solving.pdf

http://ellerbruch.nmu.edu/classes/cs255w02/cs255students/acattron/p1

1/lesson.pdf

http://www.justforkidsonly.com/mathmoney2.htm

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http://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://ellerbruch.nmu.edu/classes/cs255w02/cs255students/acattron/p11/lesson.pdfhttp://ellerbruch.nmu.edu/classes/cs255w02/cs255students/acattron/p11/lesson.pdfhttp://www.justforkidsonly.com/mathmoney2.htmhttp://www.justforkidsonly.com/mathmoney2.htmhttp://ellerbruch.nmu.edu/classes/cs255w02/cs255students/acattron/p11/lesson.pdfhttp://ellerbruch.nmu.edu/classes/cs255w02/cs255students/acattron/p11/lesson.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdfhttp://www.spring-ford.net/staff/hsmit/5th%20Grade%20Math/5thgradeeduplaceworksheets/Unit%206%20Geometry%20and%20Measurement/15_7%20Problem%20Solving%20Make%20a%20Model%20Tesselate%20a%20Hexagon%20Problem%20Solving.pdf


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basic math presentation - building a model

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