### Recognize number patterns and relationships

Explore patterns, properties and relationships involving numbers. Recognize and describe number patterns.

Get your students engaged in simplifying and solving linear equations using Mangahigh’s math game ‘Jabara’. Students start by collecting constants and dealing with zeros, dynamically seeing the results of algebraic manipulation. They progress onto dealing with unknown terms on both sides of an equation, negative terms, brackets and fractions within linear equations.

Example of blended learning lesson

Play through the first 10 levels of Jabara with the whole class on the whiteboard. This will introduce them to the basic principles of the game. Challenge the students to predict the outcome of each move in advance.

Set two ‘Jabara’ activities to your class called ‘Simplifying constants’ and ‘Adding to both sides’. Move through the class offering help where needed and challenge students to explain their solutions. Use your Mangahigh analytics platform to check progress and support struggling target struggling students.

What have they learnt about solving equations? What types of equations have they seen? What might harder equations look like?

Students return to the ‘Jabara’ activities. For the most able, set an additional activity ‘Coefficients, like terms, multiplying constants’. Use your Mangahigh analytics platform to identify any students who have struggled with the first activity ‘Simplifying constants’ and support them or encourage them to work with their peers.

Write 5 equations on the board, students attempt to solve them on paper

Introduce your students to algebraic substitution through the use of Mangahigh’s adaptive quiz ‘Substitute whole numbers into algebra’. Students will start with ‘Easy’ questions to help introduce new ideas and then move onto ‘Medium’ questions with some scaffolded support. Students then progress onto ‘Hard’ questions that really test their understanding, and the most able will move on to ‘Extreme’ questions that will challenge even the brightest students.

Example of blended learning lesson

On the whiteboard write down three algebraic expressions and associated values for substitution:

- 3x - 4 where x = 5
- 2a + 3b where a = 1
- 2(ab - 1) where a = 0

Set the Mangahigh activity ‘Substitute whole numbers into algebra’. Each time students play through the activity they will answer 10 questions. Encourage students to make at least three attempts, i.e. attempt at least 30 questions. Students will receive a bronze medal award and thus demonstrate they have a secure understanding if they can prove their competency at the hard questions. The most able students might achieve a silver or gold medal by answering extreme questions. Move through the class offering help where needed and challenge students to explain their solutions. Use your Mangahigh analytics platform to check progress and support struggling students.

Play through the activity ’Substitute whole numbers into algebra’ from your Mangahigh teacher platform on the whiteboard with the whole class. Challenges students to explain their solutions

Students return to the ‘Substitute whole numbers into algebra’ activity. For the most able, set an additional activity ‘Substitute whole numbers into algebra using indices’. Use your Mangahigh analytics platform to identify any students who have struggled with the first activity ‘Substitute whole numbers into algebra’ and support them or encourage them to work with their peers.

Ask students to find the missing values in this table for the expression (3a - b). Students attempt to solve them on paper and find more than one solution if possible.

Curriculum-aligned activities

Explore patterns, properties and relationships involving numbers. Recognize and describe number patterns.

Propose a general statement involving numbers; identify examples for which the statement is true or false.

Multiply terms together without brackets or simplify products in brackets to a positive integer power by considering repeated multiplication.

Multiply with two brackets, both form (x+a) or (x-a), including adding and subtracting the results of bracket multiplication in order to simplify. Include squaring a linear bracket of form (x+a) or (x-a).

Represent the solutions of an inequality in one variable on a number line.

Write quadratic expressions in the form (x + a)^2 + b including those with non integer ‘a’ and ‘b.

We’re loved by both teachers and students globally. Here’s the proof!

It is easy to differentiate my instruction based on a huge base of quizzes that I can access across grade levels. My higher kids can be challenged and my lower level kids can be remediated, all within your site.

I have used Mangahigh in my classroom for over 5 years. What keeps me coming back are the math games and wide range of concepts that are offered. But the best part is the fact that the kids LOVE to play it. I have students beg me to assign them Teacher Challenges! Begging for more math work? I am ok with that!!

Unlike similar products we have tested, Mangahigh generates incredible enthusiasm among the students resulting in hours of instruction done both at home and on campus, initiated by the students themselves.