When modeling the pattern with tiles, you do not need to start over again to show each growth stage — just continue building the previous stage. This is a repeating and growing pattern that can be made by squaring the odd numbers and repeating each term twice. Children might look at the overall pattern as the number of tiles increases. Encourage children to find the difference between the totals in order to discover the number of tiles added each time.
When recording the differences, they may also notice that the pattern increases by multiples of 4 4 is added first, then 8, then 12 then 16, and so on. There are 49 blue tiles and 36 black tiles for a total of 85 tiles. Some students may notice that there are 7 blue tiles along one edge and that this is the 7th stage, for a total of 7 X 7 or 49 blue tiles. Some kids may need to use algebra calculator to help them discover patterns such as the difference or sum of different colors of tiles.
Some students may complete the growth sequence but not identify the pattern of colored tiles. They would benefit from deconstructing the pattern and assembling the tiles into arrays. Extension to this activity can be to ask kids to use the rule they have discovered to find out the number of tiles in stage 20 without having to extend the chart or using the manipulatives. Solving this new problem will help to deepen their understanding of the pattern. A variation on the design growth pattern activity is to provide kids with tiles of a third color and ask them to add tiles in this color to the existing weave patterns to create squares.
Ask them to model the first three stages, just as they did in the original design growth activity.
They should record their results in a table and then look for patterns and develop algebra rules for sequences. Algebra worksheets asking exploratory questions or plotting graphs for all stages of each color can be provided along with this learning activity to provide more algebra practice problems to kids. In this learning activity, kids explore the concept of equality and variables. In the context of a literature connection, students use symbols and letters to represent the masses of different animals and to investigate relationships and express them algebraically.
Students identify relationships between the masses of the animals and write math equations that represent balanced tug-of-war teams. Solving algebraic equations is also achieved through this activity.
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Prior to this learning activity, children should have had some experience in using variables symbols or letters in algebraic expressions, and in modeling with concrete materials. Ask kids to brainstorm ways they could represent each animal without having to draw each animal. They may suggest using letters, shapes, or graphics. How many different ways can the animals combine on either side of the teeter totter to make the teeter totter balance if you have a fox, 4 turtles, and 6 squirrels?
Deeper learning can be achieved by doing pre algebra worksheets, algebra word problems, and most importantly by asking exploratory questions throughout the activity. Adding a squirrel S to both sides maintains the balance. Now rearrange the letters on each side of the equation, as follows:. Ask kids to consider whether the new algebra equations are true. Quadratic Sequences Deduce expressions to calculate the nth term of quadratic sequences. Recurring Decimals Change recurring decimals into their corresponding fractions and vica versa.
Simultaneous Solutions Arrange the given pairs of simultaneous equations in groups to show whether they have no solution, one solution or infinite solutions. Stable Scales Ten balance puzzles to prepare you for solving equations. Substitution Substitute the given values into the algebraic ex pressions. Superfluous Find a strategy to figure out the values of the letters used in these calculations.
Think of a Number Ten students think of a number then perform various operations on that number. You have to find what the original numbers were. Words and Concepts Fill in the missing words to show an understanding of the vocabulary of equations, inequalities, terms and factors. Writing Expressions Listen to the voice saying the algebraic expression then write it in its simplest form.
Calendar Maths Investigation Investigate the connection between the numbers in a T shape drawn on this month's calendar. Crossing the River Two men and two boys want to cross a river and they only have one canoe which will only hold one man or two boys. Lamp Posts What is the greatest number of lamp posts that would be needed for a strange village with only straight roads? Steps Investigate the numbers associated with this growing sequence of steps made from Multilink cubes. Simultaneous Equations Elimination This video demonstrates how to solve simultaneous equations by elimination.
Simultaneous Equations Substitution This video demonstrates how to solve simultaneous equations by substitution. Project for the whole class to see then insert the working in your own style. How old was Diophantus? An ancient riddle which can be answered by solving an equation containing fractions.
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Add 'em Add up a sequence of consecutive numbers. Can you find a quick way to do it? Arithmagons This lesson starter requires pupils to find the missing numbers in this partly completed arithmagon puzzle. Cars Calculate the total cost of four cars from the information given. Chin-Ups Work out the number of chin ups the characters do on the last day of the week give information about averages.
Christmas Presents Work out the total cost of five Christmas presents from the information given. Connecting Rules Give 20 rules connecting x and y given their values. Giraffe The height of this giraffe is three and a half metres plus half of its height.
How tall is the giraffe? Half Hearted Find the number which when added to the top numerator and bottom denominator of each fraction make it equivalent to one half. Khmer's Homework Check a student's homework. If you find any of the answers are wrong write down a sentence or two explaining what he did wrong.
Know Weigh Find the weight of one cuboid by division of each colour then add your answers together. Less Than This mathematics lesson starter invites pupils to interpret a three part algebraic inequality. Light Shopping A lamp and a bulb together cost 32 pounds. Graphic subsets , recognize a graphically described subset.
Function draw , draw a function using the graph of another, requires java. Segfrac , split a fraction into sum of fractions with smaller denominators. OEF geometric integral , collection of exercises on geometric applications of definite integrals of one variable. Popup calculator forms , you can search calculating forms or insert them into your own web pages. Quizz integration , elementary questions on integration. OEF several variables functions , collection of exercises on several variables functions. Two squares , decompose an integer into sums of two squares.
Taylor , algebraic manipulations of Taylor expansions. Quizz vector spaces , elementary questions on vector spaces. Accordance , find a polynomial according to its values. Epsilon , on the definition of continuity: given epsilon, find delta. Vision 4D , plots hypersurfaces etc. Linear system dialog , ask questions to get information in order to solve linear systems.
Order arrangement , arrange given numbers according to their order. OEF derivative , practising with differentiation. OEF triangles , collection of exercises on triangles. Linear shoot , click on the image of a point by a linear transformation. OEF vector space definition , collection of exercices on the definition of vector spaces. SQRT shoot , locate square, cubic, OEF Determinant , collection of exercises on the determinant of a square matrix.
Rank filler , complete a matrix for a minimal rank. Matrix dialog , ask questions to get information in order to solve problems on matrices. OEF vector subspaces , collection of exercises on vector subspaces. Tangent parameters , find the curve having a given tangent.
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