problem solving draw to join shapes

Maths with David

Problem solving. draw diagram.

In mathematics, diagrams are often a useful way of organising information and help us to see relationships. A diagram can be a rough sketch, a number line, a tree diagram or two-way table, a Venn diagram, or any other drawing which helps us to tackle a problem.

Labels (e.g. letters for vertices of a polygon) are useful in a diagram to help us be able to refer to items of interest.

A diagram can be updated as we find out new information.

Examples of using a diagram to tackle a problem

First we will read all three examples and have a quick think about them and then we will look at how a diagram can help us with each one:

Restaurant Example

A restaurant offers a “business lunch” where people can choose either fish or chicken or vegetables for their main course, accompanied by a side portion of rice, chips, noodles or salad. How many different combined meals can they choose between?

Rectangle Area Example

To the nearest centimetre, the length and width of a rectangle is 10cm and 8cm.

• What are the limits of accuracy for the area of the rectangle?
• the lengths of the sides?

Prime Numbers Example

Masha says that if she writes out numbers in rows of six then all of the prime numbers will either be in the column that has 1 at the top, or they will be in the column that has 5 at the top. How can you find out if she is correct?

Worked Solutions to Examples

One way to tackle this would be to write out a list, being systematic to ensure that all combinations are considered.

Another is to draw out a diagram like the one below. As shown, you actually don’t need to finish the diagram in order to conclude how many combinations there are:

You could also use a 2-way table as shown below:

Drawing a rough sketch of the rectangle labelled with the boundaries of its side lengths can really help us to visualise the situation here:

It can then be helpful to draw sketches of the smallest possible rectangle and the largest possible rectangle:

We can now answer the questions, so (a) the smallest possible area is 7.5 x 9.5 = 71.25cm 2 and the largest “possible” area is 8.5 x 10.5 = 89.25cm 2 . So the limits of accuracy are [71.25,89.25) cm 2 .

For (b), we can see from the sketches that the difference between the minimum and the maximum values is 1cm in the case of both the width and the lenght. For part (ii) we simply subtract the numbers above to give 89.25-71.25 = 18cm 2 .

Here, listing out numbers, especially for the first few is going to be helpful. We should list them as specified in the question, and we can highlight the prime numbers:

Because we know that no even numbers other than 2 are prime, we know that further prime numbers cannot be in the second, fourth or sixth column. The third column keeps adding 6s, so it is adding multiples of 3 to multiples of 3, so the numbers will always be divisible by 3, so further numbers in this column cannot be prime. So she is correct that the prime numbers must be in the first or the fifth column.

31 Questions of increasing difficulty

1.) In a cement factory, cement bags are placed on pallets made of planks of wood and bricks. The number of bricks needed to make a pallet is calculated as being one more than the length of the plank in metres (as shown below):

a.) What length of pallet uses five bricks?

b.) If the pallet is 7m long, how many bricks are used in it?

The factory needs pallets with a total length of 15m for the next batch of cement. It has planks of wood that are 4m long and 3m long.

c.) What combinations of planks can they have?

d.) How many bricks would be needed for each combination?

2.) Sonia wants to plant an apple tree in her garden. She needs to make sure that there is a circular area of lawn with diameter 3m around the base of the tree, so that all of the fruit will fall onto the lawn area.

Below is a (not to scale) sketch of Sonia’s garden:

Where could the tree be placed to meet her requirements?

3.) The diagram below represents towns A and B in a mountainous region:

The mountain rescue helicopters from both towns will always be sent to rescue any casualty within a 25km radius of town A or town B. The fire and rescue team from town B will travel to any accident scene closer to town B than town A.

Shade the region that the helicopters and town B’s fire an rescue team will both cover.

4.) A rectangle has length (2x+3) and width (x-1).

a.) Write an expression for the perimeter of the rectangle.

b.) Write an expression for the area of the rectangle.

The area of the rectangle is 250cm 2 .

c.) How long is the longest side?

d.) What is the perimeter of the rectangle?

5.) The probability that Hannah catches the 6.30am train to the city is 0.7.

If she misses the train, she will be late for work.

The probability that the train will be late is 0.15.

If the train is late, she will be late for work.

What is the probability that Hannah will be on time for work on a particular day?

6.) Two five-sided spinners are numbered 1 to 5. When the arrows are spun, your total score is calculated by adding the two numbers that the spinners land on.

a.) Draw a suitable diagram to show all possible outcomes when spinning these spinners.

b.) What is the highest score you could get?

c.) What is the probability of getting a total score of 8?

Worked Solutions to Questions

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Put Shapes Together

Warm up with a Mystery Math Mistake to tell whether Dotson’s 10-frames represent a number more than his focus number. Examine a train to find shapes. Put together shapes to make familiar objects.

Math Mights was adapted from IM K-5 Math™ ©2021 by Illustrative Mathematics® , released under the Creative Commons Attribution 4.0 International License (CC BY 4.0) https://creativecommons.org/licenses/by/4.0/.

Additions and adaptations are ©2021 by Strategic Intervention Solutions, LLC

Lesson Standards

Count to answer “how many?” questions about as many as 20 things arranged in a line, a rectangular array, or a circle, or as many as 10 things in a scattered configuration; given a number from 1-20, count out that many objects.

Analyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/“corners”) and other attributes (e.g., having sides of equal length).

Model shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.

Compose simple shapes to form larger shapes. For example, "can you join these two triangles with full sides touching to make a rectangle?”

Related Lessons

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Go Math Grade K Answer Key Chapter 9 Identify and Describe Two-Dimensional Shapes

Hello Students!!! Are you looking for the Go Math Answer Key for Grade K? If our guess is correct, then your weight is over. Because we provide the solutions for all the questions in a simple way in Go Math Grade K Answer Key Chapter 9 Identify and Describe Two-Dimensional Shapes. This helps teachers and parents to make their children complete homework or assignments in time.

Go Math Grade K Chapter 9 Answer Key Identify and Describe Two-Dimensional Shapes

Students must get an interest in math from childhood itself. So make your children fall in love with math by showing the Go Math Grade K Chapter 9 Answer Key Identify and Describe Two-Dimensional Shapes. By following our HMH Go Math Answer Key your child will get the knowledge slowly by seeing the solved images. So, Download Go Math Grade K Solution Key Chapter 9 Identify and Describe Two-Dimensional Shapes pdf for free.

Identify and Describe Two-Dimensional Shapes

Identify and Describe Two-Dimensional Shapes Show What You Know

Identify and describe two-dimensional shapes vocabulary builder, identify and describe two-dimensional shapes game number picture.

Lesson: 1 Identify and Name Circles

Lesson 9.1 Identify and Name Circles

Identify and name circles homework & practice 9.1.

Lesson: 2 Describe Circles

Lesson 9.2 Describe Circles

Describe circles homework & practice 9.2.

Lesson: 3 Identify and Name Squares

Lesson 9.3 Identify and Name Squares

Identify and name squares homework & practice 9.3.

Lesson: 4 Describe Squares

Lesson 9.4 Describe Squares

Describe squares homework & practice 9.4.

Lesson: 5 Identify and Name Triangles

Lesson 9.5 Identify and Name Triangles

Identify and name triangles homework & practice 9.5.

Lesson: 6 Describe Triangles

Lesson 9.6 Describe Triangles

Describe triangles homework & practice 9.6.

Mid-Chapter Checkpoint

Identify and Describe Two-Dimensional Shapes Mid-Chapter Checkpoint

Lesson: 7 Identify and Name Rectangles

Lesson 9.7 Identify and Name Rectangles

Identify and name rectangles homework & practice 9.7.

Lesson: 8 Describe Rectangles

Lesson 9.8 Describe Rectangles

Describe rectangles homework & practice 9.8.

Lesson: 9 Identify and Name Hexagons

Lesson 9.9 Identify and Name Hexagons

Identify and name hexagons homework & practice 9.9.

Lesson: 10 Describe Hexagons

Lesson 9.10 Describe Hexagons

Describe hexagons homework & practice 9.10.

Lesson: 11 Algebra • Compare Two- Dimensional Shapes

Lesson 9.11 Algebra • Compare Two- Dimensional Shapes

Algebra • compare two- dimensional shapes homework & practice 9.11.

Lesson: 12 Problem Solving • Draw to Join Shapes

Lesson 9.12 Problem Solving • Draw to Join Shapes

Problem solving • draw to join shapes homework & practice 9.12.

Review/Test

Identify and Describe Two-Dimensional Shapes Review/Test

DIRECTIONS Play with a partner. Decide who goes first. Toss the number cube. Color a shape in the picture that matches the number rolled. A player misses a turn if a number is rolled and all shapes with that number are colored. Continue until all shapes in the picture are colored.

Identify and Describe Two-Dimensional Shapes Vocabulary Game

DIRECTIONS Place game pieces on START. Play with a partner. Take turns. Toss the number cube. Move that many spaces. If a player can name the shape and tell something about the shape, the player moves ahead 1 space. The first player to reach FINISH wins.

The Write Way DIRECTIONS Choose two shapes. Draw to show what you know about the shapes. Reflect Be ready to tell about your drawing.

Essential Question How can you identify and name circles?

Share and Show

Problem Solving • Applications

HOME ACTIVITY • Have your child show you an object that is shaped like a circle.

Essential Question How can you describe circles?

Listen and Draw

HOME ACTIVITY • Have your child describe a circle.

Essential Question How can you identify and name squares?

HOME ACTIVITY • Have your child show you an object that is shaped like a square.

Essential Question How can you describe squares?

HOME ACTIVITY • Have your child describe a square.

Essential Question How can you identify and name triangles?

HOME ACTIVITY • Have your child show you an object that is shaped like a triangle.

Essential Question How can you describe triangles? Answer: A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry.

Concepts and Skills

Essential Question How can you identify and name rectangles?

HOME ACTIVITY • Have your child show you an object that is shaped like a rectangle.

Essential Question How can you describe rectangles?

HOME ACTIVITY • Have your child describe a rectangle.

Essential Question How can you identify and name hexagons?

HOME ACTIVITY • Draw some shapes on a page. Include several hexagons. Have your child circle the hexagons.

Essential Question How can you describe hexagons?

HOME ACTIVITY • Have your child describe a hexagon.

Essential Question How can you use the words alike and different to compare two-dimensional shapes?

HOME ACTIVITY • Describe a shape and ask your child to name the shape that you are describing.

Essential Question How can you solve problems using the strategy draw a picture?

Unlock the Problem

Try Another Problem

On Your Own

HOME ACTIVITY • Have your child join shapes to form a larger shape, and then tell you about the shape.

Conclusion:

We believe that the information presented in this article is satisfactory for you to learn the basics from now itself. Help your kids to enhance their math skills by downloading the HMH Go Math Grade K Answer Key of all chapters. Stay tuned to get the latest updates of all Go Math Grade K Solution Keys.

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