*a) If the figure has 7 dots then it has 6 (6 × 5) = 36 lines. d) A quarter of the lake covered with lilies in week 15 You can use the free Mathway calculator and problem solver below to practice Algebra or other math topics.b) If the figure with 12 dots then it has 6 (11 × 5) = 61 lines. d) If half of the lake was covered with lilies in Week 16, then in which week was a quarter of the lake covered with lilies? Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.Sometimes the problem is too difficult to solve in one step.*

When students use this strategy, they will make a reasonable guess, based on the information that they have been given and then check to see if their guess is correct The guesses should get closer and closer to the answer, until the correct answer is found.

Using a table is a good way to sort out and organise the information that has been given in the question.

d) How many dots are there for a figure with 136 lines?

The pattern is first dot 6 lines; each additional dot adds 5 lines.

A collection of 200 graded mathematical problems suitable for improving the problem solving skills of your secondary school maths students. ) With this resource your students will • improve their mathematical problem solving skills • deepen their interest in mathematics and its applications • see cross-curricular links between mathematics, the sciences, engineering, technology and other subject areas • develop their appreciation of the rich history and diverse internationalism of mathematics The tasks in this resource can be used to enrich your teaching in many ways; as a problem wall display, as a classroom activity, as extension work, as supplementary homework or as the base of an extended research project.

Anyone who has taught maths for any length of time will know how difficult it can be to teach pupils to solve maths problems out of context. There are a number of strategies that can be used to solve maths problems, as follows: Creating a diagram can help mathematicians to picture the problem and find the solution.Once the students can see all of the possibilities for the solution, they can then attempt to solve the problem more easily.This strategy requires students to use the information they have been given in the question to eliminate possible solutions to finally discover the correct solution.Giving children the experience of using these maths problem solving strategies will provide themv with a really useful toolkit for their maths arsenal as well as making them more confident when presented with a maths problem.The following are some examples of problem solving strategies.Explore it//Act it/Try it (EAT) method (Basic) Explore it//Act it/Try it (EAT) method (Intermediate) Explore it//Act it/Try it (EAT) method (Advanced) Finding a Pattern (Basic) Finding a Pattern (Intermediate) Finding a Pattern (Advanced) In this lesson, we will look at some basic examples of Find a Pattern method of problem solving strategy.a) How many lines are there if the figure has 7 dots?Working backwards is an excellent strategy to use when the final outcome of the problem has already been given.Students just need to work out what the events were that occurred previously.In Years 7–8, students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.In Years 9–10, students formulate and solve problems when they use mathematics to represent unfamiliar or meaningful situations, when they design investigations and plan their approaches, when they apply their existing strategies to seek solutions, and when they verify that their answers are reasonable.

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