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CONSOLIDATED MATH LAB ACTIVITIES GRADE 6 h�p://www.mathbuddyonline.com

DisclaimerThis document is issued in confidence only for the purpose for which it is supplied. Noinforma�on as to the contents or subject ma�er of this document or any part thereof, arisingdirectly or indirectly there from shall be reproduced, given orally or in wri�ng or communicatedin any manner to any third party being an individual, firm, company or employee thereof,without the prior wri�en consent of Concept Learning Technologies Pvt. Ltd.Copyright © 2011-2018 by Concept Learning Technologies Pvt. Ltd, All rights reserved.

PREFACEMathema�cs is all around us and we interact with the elements of mathema�cs world on a day today basis. It is a well known fact that students mathema�ze by making sense of their world inquan�ta�ve as well as qualita�ve ways. They hypothesize, make conjecture, contemplate differentscenarios, review conclusions and communicate their understanding as they interact with theenvironment. Math Lab provides an environment that fosters strong learning and engagement. Whenstudents model mathema�cal concepts, they are able to visualize pa�erns and rela�onships whichhelp them make a connec�on between the concrete and the abstract.Math Lab instruments have been designed to help students reason about mathema�cal ideas in aconcrete way and engage students’ interest. Students will not however know how to use a specifictool and will require the help of the teacher to understand how to model concepts using these tools.Math Buddy Teacher Ac�vity Math Lab Manual, presents teaching strategies and step by stepguidance to the teachers on how to effec�vely “set the stage” for performing ac�vi�es using theseinstruments. The tone and language of each ac�vity is simple and user friendly, to help teachers increa�ng an experien�al learning environment for the students.The ac�vi�es are designed and developed to help model and illustrate concepts using the variousinstruments. Ac�vi�es are supplemented with observa�on sheets whereby students must recordtheir observa�ons and findings. Observa�on sheets guide the students in their explora�on processand enable teachers to gauge their understanding of the mathema�cal concepts as well as iden�fyareas of improvements. Each ac�vity has a specific learning objec�ve and outlines the skills thatstudents will develop.The ac�vi�es in this manual also correlate very well to those in the digital component –Math Buddy @School Lab. It is recommended that teachers let the students explore each conceptwith the hands-on ac�vity for that concept, followed by reinforcement with digital interac�veac�vi�es in the classroom that have been designed to encourage student par�cipa�on anddiscussion.Every effort has been made to align this ac�vity manual to the Guidelines for Maths Laboratories inSchools as suggested by NCERT in the Na�onal Curriculum Framework (NCF) for School Educa�onand we have tried our best to comprehensively cover all the important concepts.We strongly feel that a mathema�cs lab enables students to build deep seated interest andconfidence in the subject as well as reduce the associated abstractness that comes along withmathema�cs learning. We welcome any feedback, sugges�ons and ideas from you for furtherimprovement of this manual.The Math Buddy Team

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Contents1. Integer addi�on using chips 12. Integer subtrac�on using chips 53. Integer mul�plica�on with chips 114. Integer division with chips 155. Equivalent ra�os and Propor�ons 196. Tower of Brahma 247. Collinear and Non-Collinear Points 288. Parallel and Perpendicular Lines 329. Making different types of triangles with anglegs 3710. Making different types of quadrilaterals with anglegs 4011. Understand a circle and its parts 4612. Prisms and Pyramids using Geoboard 5413. Classifying polygons 6614. Reflec�on Symmetry 6915. Tessella�on Pa�erns 7916. Puzzling Pentominoes III 86

ACTIVITY 1: INTEGER ADDITION WITH CHIPSLearning Objec�ves: Students will understand the concept behind addi�on of integers bymodeling them with two coloured chips.Materials required: Blue and red chips, Integer addi�on board.Teaching strategy:1. This is an abstract concept that students find difficult to relate to, especially with them just ge�ng introduced to the concept of nega�ve numbers.2. We will use two coloured chips to model integers. Posi�ve integers need to be represented using blue chips, while nega�ve integers need to be represented using red chips. They will model these on the integer addi�on board. PN3. Write an integer addi�on problem on the board, say 4 + (-3) and ask the students to model it on the integer addi�on board. To model 4, they will need to place four blue chips in the first columns, and to model -3, they will need to place three red chips in the second column. Zero pair 1st Integer 2nd Integer Sum of the Removed two Integer Zero pair PN PN PN P Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 1 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 1: INTEGER ADDITION WITH CHIPS4. Now, ask them to move the chips from both the columns to the third column. Ask them to form as many pairs of red and blue chips. These pairs having a combina�on of blue (+1) and red (-1) chips have a value of zero and are called zero pairs.5. Ask them to remove all the zero pairs and place them in the fourth column. The chips remaining in the third column a�er all the zero pairs are removed represent the sum of the given integers.6. They can follow the same procedure for finding the sum of any two integers.7. To solve the ques�ons in the observa�on sheet, they need to model the ques�on using chips on the integer addi�on mat and then colour the circles to represent the same on paper. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 2 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 1: INTEGER ADDITION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. Represent the first integer and the second integer on the Integer Addi�on board using the red and blue chips given. Posi�ve integers need to be represented using blue chips and nega�ve integers using red.2. Remove all possible pairs of red and blue chips from the two columns.3. Count the number of chips remaining the first and second columns and write the result.1. Find the sum of -5 and 6. Colour the chips with RED or BLUE colour to represent the numbers.First numberSecond numberNumber of zero pairs:Sum of the two numbers:2. Find the sum of -4 and -7. Colour the chips with RED or BLUE colour to represent the numbers. First number Second numberNumber of zero pairs:Sum of the two numbers:Math Buddy 3 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 1: INTEGER ADDITION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:3. Find the sum of 4 and 7. Colour the chips with RED or BLUE colour to represent the numbers.First number Second numberNumber of zero pairs:Sum of the two numbers:Educator’s Comment Date SignatureMath Buddy 4 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 2: INTEGER SUBTRACTION WITH CHIPSLearning Objec�ves: Students will understand the concept behind subtrac�on of integers bymodeling them with two coloured chipsMaterials required: Blue and red chips, Integer subtrac�on board.Teaching strategy:1. This is an abstract concept that students find difficult to relate to – especially on how the value of a number goes up when a posi�ve number is added to it as well as when a nega�ve number is subtracted from it. Modeling helps remove some of the abstractness and gives some life to the concept.2. We will use two coloured chips to model integers. Posi�ve integers need to be represented using blue chips, while nega�ve integers need to be represented using red chips. They will model these on the integer subtrac�on board. PN3. Write an integer subtrac�on problem on the board, say 4 – 3. Ask the students the meaning of the term ‘subtrac�on’ and engage them in a discussion �ll they agree that subtrac�on means ‘taking away’. In this case, we need to ‘take away’ 3 blue chips from 4 red chips.4. Ask the students to model the first integer in the first column of the integer subtrac�on board. We need to remove 3 of these blue chips Zero pair Integer Represented Integer Subtracted P P P P Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 5 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 2: INTEGER SUBTRACTION WITH CHIPS5. Now, ask them to remove the required number of chips and place them in the second column.6. The number and colour of the chips remaining in the first column represents the result of the subtrac�on.7. The subtrac�on problem gets a li�le interes�ng when there are not enough chips to remove. Let us see how we can model and solve such problems. For example, let us find the result of (3 – 5). Get the students to place 3 blue chips in the first column. Zero pair Integer Represented Integer Subtracted P P P Ask the students the meaning of the statement 3 – 5. Get them to see that this means thatwe need to remove 5 blue chips from 3 blue chips. However, there are only 3 blue chips. How do we remove 5 blue chips from these? We use the concept of zero pairs. The value of a number does not change if we add zero pairs to it.8. Ask them how many zero pairs need to be added. Get them to say that we need to add 2 zero pairs because we need two more blue chips to find a solu�on to the subtrac�on problem. Add two zero pairs to the first column. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 6 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 2: INTEGER SUBTRACTION WITH CHIPS Zero pair Integer Represented Integer Subtracted PN PN P P PNow we have enough blue chips to remove. Remove the five blue chips and placethem in the second column. There are two red chips remaining in the first column,which represents the result of the subtrac�on. The result of the subtrac�on istherefore -2. Zero pair Integer Represented Integer Subtracted NP NP P P P9. This process can be used to solve any integer subtrac�on problem. The students will also get a feel for the use of zero pairs.10. For every ques�on, ask the students to write the meaning of the statement in terms of chips. For example: 7 – (-5) means taking away 5 red chips from 7 blue chips. -8 – 4 means taking away 4 blue chips from 8 red chips. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 7 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 2: INTEGER SUBTRACTION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. Represent the first integer on the first column of the Integer Subtrac�on board using the red and blue chips given. Posi�ve integers need to be represented using blue chips and nega�ve integers using red.2. Look at the second integer and remove as many chips as required from the first column to represent the second integer. If there are not enough chips of the required colour available, add zero pairs (pairs of red and blue chips) �ll you have enough chips to represent the second integer.3. Count the number of chips remaining in the first column and write the result.1. Let us subtract: 8 – 5 What does this statement mean in terms of chips? Represent the first number: Are there enough chips of the required colour to remove? Yes/No Do we need to add any zero pairs? __________How many zero pairs? __________ Represent first number with zero pairs: __________ Strike out the chips to be removed. How many chips are remaining? Therefore, 8 – 5 = _______2. Let us subtract: 5 –8 What does this statement mean in terms of chips?Math Buddy 8 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 2: INTEGER SUBTRACTION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Represent the first number:Are there enough chips of the required colour to remove? Yes/NoDo we need to add any zero pairs? __________ How many zero pairs? __________Represent first number with zero pairs: __________ Strike out the chips to be removed. How many chips are remaining? Therefore, 5 – 8 = _______3. Let us subtract: 8 – (-5) What does this statement mean in terms of chips? Represent the first number: Are there enough chips of the required colour to remove? Yes/No Do we need to add any zero pairs? __________ How many zero pairs? __________ Represent first number with zero pairs: __________ Strike out the chips to be removed. How many chips are remaining? Therefore, 8 – (-5) = _______4. Let us subtract: -8 –5 What does this statement mean in terms of chips?Math Buddy 9 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 2: INTEGER SUBTRACTION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Represent the first number:Are there enough chips of the required colour to remove? Yes/NoDo we need to add any zero pairs? __________ How many zero pairs?__________Represent first number with zero pairs: __________Strike out the chips to be removed.How many chips are remaining?Therefore, -8 – 5= _______Educator’s Comment Date SignatureMath Buddy 10 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 3: INTEGER MULTIPLICATION WITH CHIPSLearning Objec�ves: Students will understand the concept behind mul�plica�on of integersby modeling them with two coloured chips.Materials required: Blue and red chips, Opera�ons board.Teaching strategy:1. Begin the discussion with the meaning of the term ‘mul�plica�on’ and how it is basically repeated addi�on of numbers.2. In mul�plica�on, there are two components – mul�plicand (the number being mul�plied) and the mul�plier. For example, if we want to mul�ply 6 x -3, the mul�plicand is -3 and the mul�plier is 6.3. Tell the students that we will use two coloured chips to model integers. Posi�ve integers need to be represented using blue chips, while nega�ve integers need to be represented using red chips. Blue Red4. First, ask the students to represent the mul�plicand along the top row of the opera�ons board. In the example -6 x -3, they need to place 3 red chips to represent the mul�plicand. Red Red Red Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 11 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 3: INTEGER MULTIPLICATION WITH CHIPS5. Ask the students to ignore the sign of the mul�plier for now. They need to repeat the chips represented by the mul�plicand as many �mes as the mul�plier. Repeat 6 Red Red Red �mes Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red6. Now, ask the students to look at the sign of the mul�plier. If it is posi�ve, they need to leave the chips as they are. If it is nega�ve, they need to replace all the chips inside the board with those of opposite colour. Replace red chips with blue chips and vice versa. In our example of -6 x -3, the sign is nega�ve. Therefore, they need to replace all the red chips inside with blue chips. Red Red Red Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue7. Ask them to see that that there are 18 blue chips inside and therefore, the result of mul�plying -6 x -3 = +18.8. Students can follow the same procedure to find the result of mul�plying an integer by another integer. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 12 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 3: INTEGER MULTIPLICATION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. In mul�plica�on, there are two components – mul�plicand (the number being mul�plied) and the mul�plier. For example, if we want to mul�ply 6 x -3, the mul�plicand is -3 and the mul�plier is 6.2. Ignore the colour of the mul�plier and repeat the chips represented by the mul�plicand as many �mes as the mul�plier.3. Flip the colour of the chips inside the board if the sign of the mul�plier is nega�ve.4. The number and colour of chips inside the board represents the result.No. Mul�plica�on A�er Step 1: A�er Step 2: A�er Step 3: Step 4: 1 Problem Number and Number and Number and Product colour of chips colour of the chips colour of chips represen�ng the represen�ng represen�ng mul�plicand the product the product (before flipping) (a�er flipping)1 6x22 7x33 5x34 6 x -25 7 x -36 4 x -67 -6 x 28 -7 x 3 9 8 x -310 -6 x -211 -7 x -312 -6 x -3Math Buddy 13 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 3: INTEGER MULTIPLICATION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Educator’s Comment Date SignatureMath Buddy 14 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 4: INTEGER DIVISION WITH CHIPSLearning Objec�ves: Students will understand the concept behind division of integers bymodeling them with two coloured chips.Materials required: Blue and red chips, Opera�ons board.Teaching strategy:1. Begin the discussion with the meaning of the term ‘division’ and how it relates to mul�plica�on.2. In a division statement, the number being divided is called the ‘dividend’, while the number dividing it is called the ‘divisor’ and the result of the division is called the ‘quo�ent’. Ask them how these things relate to the mul�plica�on terms like ‘mul�plicand’, ‘mul�plier’ and ‘product’? The dividend is nothing but the product, while the divisor is the ‘mul�plier’ and the quo�ent is the ‘mul�plicand’.3. Tell the students that we will use blue and red coloured chips to model integers. Posi�ve integers need to be represented using blue chips, while nega�ve integers need to be represented using red chips. Blue Red4. Let us divide -18 by -3. First, ask the students to represent the divisor along the top row of the opera�ons board. In the example -18 divided by -3, they need to place 3 red chips to represent the divisor on top. Red Red Red Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 15 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 4: INTEGER DIVISION WITH CHIPS5. Next, they need to arrange the dividend. Place as many chips as the dividend inside the board in a rectangular form with each row having the same number of chips as the divisor. Use blue chips if the dividend is posi�ve and red chips if the dividend is nega�ve. Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red Red6. Ask the students to look at the sign of the divisor. If it is red, then flip the chips used for the dividend. In our example of -18 divided by -3, the divisor is -3, which is nega�ve. Therefore, they need to replace all the red chips inside with blue chips. Repeat 6 Red Red Red �mes Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue Blue7. Now, ask the students to count the number of rows of chips inside the board. The number of rows along with the colour of the chips inside gives the quo�ent. Ask them to see that that there are 6 rows of blue chips. Therefore, the quo�ent has to be +6. If the colour of the chips were to be red, the quo�ent would have been 6.Students can follow the same procedure to find the result of dividing any integer by anyother integer. Ask them to complete the ques�ons in the observa�on sheet by modelingthem with chips. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 16 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 4: INTEGER DIVISION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. In a division statement, the number being divided is called the ‘dividend’, while the number dividing it is called the ‘divisor’ and the result of the division is called the ‘quo�ent’.2. Represent the dividend by placing as many chips in a rectangular form just below thedivisor. Each row of the rectangle needs to have the same number of chips as the divisor.3. Flip the colour of the chips inside the board if the sign of the divisor is nega�ve.4. The number of rows occupied and colour of chips inside the board represents the result.No. Division A�er Step 1: A�er Step 2: A�er Step 3: Step 4: Statement Number and Number and Number and Quo�ent colour of chips colour of the chips colour of chips represen�ng the represen�ng represen�ng the dividend the divisor dividend (a�er flipping) (before flipping)1 12 ÷ 3 2 21 ÷ 7 3 25 ÷ 5 4 12 ÷ (-3) 5 21 ÷ (-7) 6 25 ÷ (-5) 7 (-12) ÷ 3 8 (-21) ÷ 7 9 (-18) ÷ 610 (-12) ÷ (-3)11 (-21) ÷ (-7)12 (-24) ÷ (-8)Math Buddy 17 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 4: INTEGER DIVISION WITH CHIPS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Educator’s Comment Date SignatureMath Buddy 18 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 5: EQUIVALENT RATIOS AND PROPORTIONS 10 cm Orange rod (ON) Blue (BE) Brown (BN) Black (BK) Dark Green (DG) Yellow (YW) Purple (PE) Light Green (LG) Red (RD) White (WE) 1 cmLearning Objec�ves: Students will model the given ra�os with Cuisenaire rods and find somepropor�onate values.Materials required: Cuisenaire Rods, Cuisenaire Representa�on Board.Teaching strategy:1. Begin the discussion in the classroom as to what students understood by the term ‘ra�o’ and ask them for some examples in everyday life where they might be using this term.2. Give an example – There were 20 ques�ons in Ram’s exam and he got 15 correct. There were 12 ques�ons in Shyam’s exam and he got 9 of them correct. Ask the students who did be�er in their exam and why? Get them to see that while Ram did well on absolute terms, ge�ng 15 out of 20 is same as ge�ng 9 out of 12, because both of them have got 3 ques�ons correct for every 4 ques�ons answered.3. Tell them that 12 out of 15 and 9 out of 12 are said to be in the same propor�on and both of them are in the ra�o 3 : 4.4. Next, give the Cuisenaire rod set to the students and get them to model ra�os and propor�ons. Each rod in the Cuisenaire set has a specific value. Have the students select the rods that have a value of 3 and 4 from the set. These should be the Light Green and Purple rods respec�vely. Ask them to note down the number of divisions in the rods in the table. 3 LG LG LG 4 PE PE PE PE Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 19 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 5: EQUIVALENT RATIOS AND PROPORTIONS5. Now, ask them to a�ach one more set of light green and purple rods, and ask the students to note down the number of divisions. Con�nue this process �ll they a�ach about 5 sets of rods. 6 LG LG LG LG LG LG 8 PE PE PE PE PE PE PE PE6. As they note down the number of divisions, tell them each pair of divisions represents a propor�on.7. Con�nue this for the other ra�os and get the students to find propor�onal values for these as well. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 20 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 5: EQUIVALENT RATIOS AND PROPORTIONS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. Iden�fy the rods corresponding to the ra�o to be represented. For example, to represent the ra�o 2 : 3, select a red rod and a light green rod.2. Using the rods iden�fied, create rod trains with same coloured rods. Connect two rods at the end, to create a rod train. At every stage, note down the number of divisions in the rod train.3. Repeat �ll each rod train has at least 5 rods.4. Each pair of numbers in the ra�o table represents a propor�on to the ra�o selected.1. Let us fill the ra�o table for the ra�o 2 : 3.Given ra�o Colour of Cuisenaire Number of rods in the rod train 2 rod selected 1 2 3 4532. Let us fill the ra�o table for the ra�o 3 : 4.Given ra�o Colour of Cuisenaire Number of rods in the rod train 3 rod selected 1 2 3 45 43. Let us fill the ra�o table for the ra�o 4 : 5.Given ra�o Colour of Cuisenaire Number of rods in the rod train 4 rod selected 1 2 3 45 5Math Buddy 21 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 5: EQUIVALENT RATIOS AND PROPORTIONS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:4. Let us fill the ra�o table for the ra�o 3 : 5.Given ra�o Colour of Cuisenaire Number of rods in the rod train 3 rod selected 1 2 3 4555. Let us fill the ra�o table for the ra�o 4 : 7.Given ra�o Colour of Cuisenaire Number of rods in the rod train 4 rod selected 1 2 3 45 76. Let us fill the ra�o table for the ra�o 5 : 10.Given ra�o Colour of Cuisenaire Number of rods in the rod train 5 rod selected 1 2 3 4510Math Buddy 22 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 5: EQUIVALENT RATIOS AND PROPORTIONS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Challenge:a) The ra�o 5 : 10 falls in the ra�o table for another ra�o. Can you tell which ra�o it is? (Clue: Find a common factor between the two numbers and divide both the numbers by that common factor).b) If you divide both the numbers in a ra�o by their greatest common factor, you will get the simplest form of the given ra�o. What is the simplest form of 8 : 16?Educator’s Comment Date SignatureMath Buddy 23 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 6: TOWER OF BRAHMALearning Objec�ves: Develop analy�cal abili�es using an interes�ng mathema�cal game.Materials required: Tower of Brahma kit.Teaching strategy:1. This is an interes�ng game that brings out the beauty of Mathema�cs and helps develop analy�cal thinking skills in children.2. The kit consists of a base with 3 pins and five discs of different diameters. The discs are arranged on the le� most pin in the order of decreasing diameters (a larger disc is always below a smaller disc). The objec�ve is to move all the discs to another pin in the least number of moves following these condi�ons: a. Only one disc can be moved at a �me b. A larger disc cannot be placed over a smaller disc c. The third pin can be used for intermediate moves3. Strategy - Have the students start with one disc and count the minimum number of moves. Try with 2 discs, 3 discs and so on. Make a note of the minimum number of moves.4. Ask them to observe any pa�ern in the minimum number of moves. a. They should see a pa�ern like this i. 1 disc – 1 move ii. 2 discs – 3 moves iii. 3 discs – 7 moves iv. 4 discs – 15 moves v. 5 discs – 31 moves. b. In general, the number of moves required for transferring ‘n’ discs is 2n – 1. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 24 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 6: TOWER OF BRAHMA5. Tell them the story of Tower of Brahma: According to Hindu Mythology, Lord Brahma had ordained a tower like this with 64 discs and had asked a number of great rishis si�ng around a sacrificial fire to transfer these discs according to the above rules from one pin to another. The work of transfer of discs was started when the earth was created and the earth will perish when the transfer process is completed. Based on the above pa�ern, it should take 264 – 1 moves. Even if it takes 1 second per move, it will take 18, 446, 744, 073, 709, 551, 615 seconds which works out to 585 billion years. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 25 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 6: TOWER OF BRAHMA OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. The kit has a base with 3 pins and five discs of different sizes.2. In the le� most pin, place the discs in the order of increasing size with the largest disc at the bo�om.3. You need to transfer all the discs to another pin following these rules a. Only one disc can be moved at a �me. b. A larger disc cannot be placed on top of a smaller disc at any point of �me. c. You can use the third pin for intermediate moves.1. Place only the largest disc on the le� pin. How many moves does it take for you to move this disc to another pin?2. Now, place 2 discs on the le� pin. Be sure to place the larger disc at the bo�om and a smaller disc above it. Following the rules given above, what is the least number of moves you will need to move the two discs to another pin?3. Fill up the table on the next page for more number of discs. Remember you need to find the MINIMUM number of moves to move all the discs to another pin while following the rules.Math Buddy 26 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 6: TOWER OF BRAHMA OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE: Number of discs Minimum number of on the le� pin moves to move all the 1 discs to another pin 2 3 4 53a. Do you observe any pa�ern in the minimum number of moves?3b. Can you tell how many moves it will take to move 6 discs based on this pa�ern?Educator’s Comment Date SignatureMath Buddy 27 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 7: COLLINEAR AND NON-COLLINEAR POINTSLearning Objec�ves: Students will be able differen�ate between collinear and non-collinearpoints.Materials required: X-Y Coordinate Board with pegs.Teaching strategy:1. Move the X and Y bars in the X-Y coordinate board to one side.2. Ask the kids to randomly place 6 pegs at various loca�ons on the board.3. Now give them a rubber band and ask them to stretch the rubber band around the pegs such that the rubber band forms a straight line.4. Some of the pegs might not fall on the straight line.5. To test whether the pegs are collinear, ask the students to count the number of pegs that lie within the rubber band. a. If the number of pegs covered by the rubber band is greater than or equal to three, then the pegs that are within the rubber band are collinear. b. The pegs that are not covered by the rubber band are non-collinear.6. Let them mark the pegs that are collinear in the grid paper given in the observa�on sheet. Let them create some more collinear and non-collinear points and make the observa�on. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 28 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 7: COLLINEAR AND NON-COLLINEAR POINTS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. In the XY coordinate board, move the X and Y bars to one side.2. Take 6 pegs and posi�on them randomly in the X-Y coordinate board.3. Take a rubber band and stretch them across the pegs such that the rubber band forms a straight line.4. If atleast three pegs are within the straight line, the pegs are collinear. The other pegs are non-collinear.5. Make an observa�on of all the collinear pegs and non-collinear pegs.1. Take 6 pegs and posi�on them randomly on the X-Y Coordinate board. Mark the posi�ons in the given grid. Name the posi�ons of the pegs as 1, 2, 3, 4, 5 and 6. Join as many pegs as possible making sure that they fall on a straight line. Leave the pegs that are outside the straight line.Math Buddy 29 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 7: COLLINEAR AND NON-COLLINEAR POINTS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:1a. Do you have atleast 3 pegs within the straight line? a. Yes b. No1b. If you have atleast 3 pegs within the straight line, the pegs are collinear. Write the pegs that are collinear and non-collinear. a. Collinear pegs are: b. Non-collinear pegs are:2. In the given grid, mark 10 points such that atleast 6 points are collinear and 4 points are non-collinear.Math Buddy 30 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 7: COLLINEAR AND NON-COLLINEAR POINTS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:3. In the given grid, say which points are collinear and which are non-collinear. a. Collinear pegs are: b. Non-collinear pegs are: 19 1 7 20 2 21 3 17 18Educator’s Comment 4 8 5 96 10 13 14 11 12 15 16 Date SignatureMath Buddy 31 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 8: PARALLEL AND PERPENDICULAR LINESLearning Objec�ves: Using a Geoboard, students will understand the proper�es of paralleland perpendicular lines.Materials required: 5 x 5 regular Geoboard, rubber bandsTeaching strategy:1. The objec�ve of this ac�vity is to help students explore and understand parallel and perpendicular lines.2. Demonstrate the Geoboard to the students. Show them that this Geoboard has 5 rows of pegs, which are spaced equally in the ver�cal and horizontal direc�ons. The distance between each pair of consecu�ve pegs is 1 unit.3. Tell the students that two lines are said to be parallel if they never meet even if extended for ever. Ask them to create a pair of parallel lines using two rubber bands on the Geoboard.4. In the observa�on sheet, there are some lines given. Ask the students to create as many parallel lines as they could for these lines.5. Now, tell them that any line that makes an angle of 90 degrees with another line is said to be perpendicular to that line. Ask the students to create a line perpendicular to any pair of parallel lines.6. Ask them to take a ruler and measure the distance between any two pairs of parallel lines. Ask them how they will measure the distance between two lines since there are many points on each line and the distance between each pair of points will give a different result. Make sure that the students understand that we always mean the shortest distance when measuring distance between two parallel lines.7. Get them to see that the shortest distance between two parallel lines is always along a line that is perpendicular to the lines. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 32 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 8: PARALLEL AND PERPENDICULAR LINES OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity ProcedureStep1: You are given a 5 x 5 geoboard. Using the rubber bands, you will need to model parallel lines and perpendicular lines by following the instruc�ons given below.Step2: As you model the lines, draw them on the grid given.Step3: Observe the proper�es of parallel and perpendicular lines and note them down.1. You are given a 5 x 5 geoboard. Using two rubber bands, can you create a pair of parallel lines on the geoboard? Draw the lines you created in the figures given below.2. What do you no�ce about these lines? If you extend these lines in either direc�on, will they ever meet?3. Now, can you model the following lines on the geoboard and create as many lines parallel to these lines on the geoboard? Draw the lines you created in the figures given below.Math Buddy 33 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 8: PARALLEL AND PERPENDICULAR LINES OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:4. Now, let us take one of the lines. Can you use a rubber band and model a line which is at an angle of 90 degrees to this line? Draw the lines you created in the figures given below.5. This new line is said to be perpendicular to the first line. There are more such lines that are perpendicular to the given line. Try to find as many as you can.6. Now, can you model the following lines on the geoboard and create as many lines perpendicular to these lines on the geoboard? Draw the lines you created in the figure given below.Math Buddy 34 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 8: PARALLEL AND PERPENDICULAR LINES OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:7. Now, let us get back to parallel lines and try to find the distance between two parallel lines. Let us say we need to find the distance between the two parallel lines given below. C B AMath Buddy 35 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 8: PARALLEL AND PERPENDICULAR LINES OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:8. How will you measure the distance between two parallel lines? Model another line that is perpendicular to the two parallel lines, and measure the length of this line inside the two parallel lines. Can you measure the distance between the two parallel lines at points A, B, and C and write down the values in the table below. No Point of Distance between measurement the parallel lines (cm) 1A 2B 3C9. What do you no�ce about the distances at points A, B and C?10. Try out other parallel lines and see if the property holds.Educator’s Comment Date SignatureMath Buddy 36 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 9: MAKING DIFFERENT TYPES OF TRIANGLES WITH ANGLEGSLearning Objec�ves: Students will understand the proper�es of different types of triangles byprac�cally construc�ng them.Materials required: Anglegs and protractor.Teaching strategy:1. Start the ac�vity by discussing the different types of triangles. Ask the students to select 3 blue strips and form a triangle. Ask them the name of the triangle that they have formed. Ask them to observe the sides and the angles of the triangle. They can use a protractor to measure the three angles of the triangles and note it down in the observa�on sheet.2. Now, ask them to replace one of the blue legs in the triangle with a red leg. Ask them what has changed in the triangle and the type of triangle just formed. They can measure the angles of the triangle and note it down in the observa�on sheet. They should see that the angles opposite to equal sides are equal since this is an isosceles triangle.3. Get the students to replace one more blue leg with a green leg and ask them the type of triangle formed. They can note down the proper�es of this triangle in the observa�on sheet.4. Now you can tell them that they need to form a right triangle from this by replacing the red leg with another colour. Ask them to iden�fy the colour that will help them create a right triangle. They need to see that replacing the red with a green leg will give a right triangle.5. Once they have formed the different types of triangles and the students have noted down the angles in each case in the observa�on sheet, ask them what they observe about the angles. They should see that the sum of angles always remains 180 degrees.6. You can ask them to create as many different triangles of each type by selec�ng different combina�ons of colours. For example, they can form an equilateral triangle by selec�ng any 3 legs of the same colour. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 37 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 9: MAKING DIFFERENT TYPES OF TRIANGLES WITH ANGLEGS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. The angle leg set contains many coloured s�cks (called as ‘legs’).2. Follow the instruc�ons in the observa�on sheet. Select different combina�ons of legs to form different types of triangles. Observe the proper�es of triangles thus formed.3. Note down your observa�ons in the observa�on sheet.No. Anglegs Type of triangle Angles at ver�ces Sum of the angles Combina�on formed (degrees) at the ver�ces (degrees) A BC1 3 Blue2 2 Blue, 1 Red3 1 Blue, 1 Red, 1 Green4 1 Blue, 2 Green5 1 Red, 1 Purple, 1 Blue6 2 Green, 1 Orange7 2 Purple, 1 Blue1. What do you observe about the angles of an equilateral triangle?2. What do you no�ce about the angles of an Isosceles triangle?3. What do you no�ce about the sum of angles at the ver�ces of a triangle?Math Buddy 38 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 9: MAKING DIFFERENT TYPES OF TRIANGLES WITH ANGLEGS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:4. Let us try to form as many combina�ons of anglegs to form the following types of triangles:No. Right Triangle Equilateral Triangle Isosceles Triangle12345678Educator’s Comment Date SignatureMath Buddy 39 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 10: MAKING DIFFERENT TYPES OF QUADRILATERALS WITH ANGLEGSLearning Objec�ves: Students will understand the proper�es of different types ofquadrilaterals by prac�cally construc�ng them.Materials required: Anglegs.Teaching strategy:1. Start the ac�vity by discussing the different types of quadrilaterals.2. Ask the students to select 4 yellow strips and form a quadrilateral. Connect the diagonals of the quadrilateral using two red strips.3. Ask them the name of the quadrilateral that they have formed. Ask them to observe the sides and the angles of the quadrilateral. The lengths of the strips are men�oned on the strips. They can use a protractor to measure the angles at the four ver�ces of the quadrilateral and note it down in the observa�on sheet.4. Now, ask the students how they can form a rhombus using these same yellow strips. Keeping the yellow strips connected, get them to remove the diagonal red strips and let the angles at the ver�ces be different from 90 degrees. They can see that the resul�ng shape is a rhombus. Ask the students the difference between the square and the rhombus.5. Get the students to replace two of the parallel yellow legs with two purple legs, and ask them to form a quadrilateral. Connect one of the diagonals using a blue leg (just to fix the angles at a right angle). Ask the students the name of the quadrilateral formed. Ask them to note down the lengths of the sides and the angles at the ver�ces in the observa�on sheet.6. Ask them to form a parallelogram from this shape. Again, they should see that removing the diagonal and changing the vertex angles away from 90 degrees makes the quadrilateral a parallelogram. Ask them to tell the differences between a rectangle and a parallelogram. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 40 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 10: MAKING DIFFERENT TYPES OF QUADRILATERALS WITH ANGLEGS7. Now, ask them to replace one of the yellow legs with an orange leg. Ask them to connect the diagonal using a yellow leg. Ask them to write down the shape formed and all the proper�es that they no�ce. Get them to measure the distance between the two parallel lines. They should see that only one pair of opposite sides are parallel. The parallel sides are of different lengths. Also, in this case, the trapezium formed is an isosceles trapezium since the non-parallel sides are of equal lengths.8. Ask them to create a non-isosceles trapezium in a similar way. One of the ways would be to remove one of the purple legs and replace with a green leg. They can connect the diagonals using another green leg.9. Now, ask the students to connect two yellow legs end to end and two orange legs at the other ends of the yellow legs. Let them a�ach a blue leg for the diagonal. Ask the students to name the quadrilateral thus formed. They should see that this forms a kite. Ask them to note down the proper�es of this quadrilateral.10. The best way for students to explore and understand the proper�es of all these quadrilaterals is to create as many of each as they can. Encourage them to create many different squares, rectangles, parallelograms, rhombuses, trapeziums and kites of different sizes. Observa�on Sheet: A framework to guide your students in the explora�on process. Encourage them to note down their observa�ons as they work with the ac�vi�es.Math Buddy 41 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 10: MAKING DIFFERENT TYPES OF QUADRILATERALS WITH ANGLEGS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:Ac�vity Procedure1. The angleg contains many coloured s�cks (called as ‘legs’).2. Follow the instruc�ons in the observa�on sheet. Select different combina�ons of legs to form different types of quadrilaterals.3. Note down your observa�ons in the observa�on sheet.1. Take 4 yellow anglegs and connect them to form a quadrilateral. Connect the diagonals of the shape formed with a red strip. 1a. What is the name of the shape formed:1b. What proper�es can you observe regarding this shape? i. Rela�ng to sides:ii. Rela�ng to angles at the ver�ces:iii. Is there any other property that you observe?2. Remove the red leg connected along the diagonal. Move the legs slightly so that the ver�ces are not at right angles any more. 2a. Now, what is the name of the shape formed?2b. What proper�es can you observe regarding this shape? i. Rela�ng to sides:Math Buddy 42 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 10: MAKING DIFFERENT TYPES OF QUADRILATERALS WITH ANGLEGS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:ii. Rela�ng to angles at the ver�ces:iii. Is there any other property that you observe?3. Replace two of the parallel yellow legs with purple legs. Connect one of the diagonals using a blue leg. 3a. What is the name of the shape formed?3b. How is this shape different from the shape in ques�on 1?3c. What proper�es can you observe regarding this shape? i. Rela�ng to sides:ii. Rela�ng to angles at the ver�ces:iii. Is there any other property that you observe?Math Buddy 43 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 10: MAKING DIFFERENT TYPES OF QUADRILATERALS WITH ANGLEGS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:4. Remove the blue leg connected along the diagonal. Move the legs slightly so that the ver�ces are not at right angles any more. 4a. Now, what is the name of the shape formed?4b. How is this shape different from the shape in ques�on 2?4c. What proper�es can you observe regarding this shape? i. Rela�ng to sides:ii. Rela�ng to angles at the ver�ces: iii. Is there any other property that you observe?5. Replace one yellow leg with an orange leg. Connect one of the diagonals using a yellow leg. 5a. What is the name of the shape formed:5b. What proper�es can you observe regarding this shape?Math Buddy 44 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18

ACTIVITY 10: MAKING DIFFERENT TYPES OF QUADRILATERALS WITH ANGLEGS OBSERVATION SHEETINSTRUMENTS USED: STUDENT NAME: GROUP NAME: DATE:i. Rela�ng to sides:ii. Rela�ng to angles at the ver�ces:iii. Is there any other property that you observe?6. Now, remove all the legs. Connect two yellow legs end to end, and two orange legs at the other ends of the yellow legs. This is a very different type of quadrilateral. 6a. Do you know the name of this shape?6b. What proper�es can you observe regarding this shape? i. Rela�ng to sides: ii. Rela�ng to angles at the ver�ces: iii. Is there any other property that you observe?Educator’s Comment Date SignatureMath Buddy 45 h�p://www.mathbuddyonline.com You can count on me ...! © Concept Learning Technologies Pvt Ltd. 2011-18