Maths with rods by Jose Maria de Cuenca

Plaay and Learn

Math hs w with rodss 40 exercisee tabss to p play w with parentts

M María Alonso Garccía Jossé Mª dee Cuenca de la Crruz 2013 3

Maths with rrods oduction Intro This book begins a collectio on that is intended to heelp those children who e enjoy workinng "a little more" at hom m me, en they comp plete their scchool day orr they have aa holiday. It is essential tto use this sshared time nicely for th hem whe and for us, theirr parents. Th he enjoymen nt of the acttivities is essential for ch hildren to deevelop a love e of learningg. If you do this at eearly stage of o his life, you y will increease the efffort they to be able to apply it in the t future, and a therrefore they m may reach their full intelllectual deveelopment. With h the activitiies of this firrst issue willl facilitate thhe developm ment of the b basic math sskills at startt of the scho ool, betw ween the mo onths of October and No ovember. Thhey are based on the use e of rods, so o we'll have tto get hold o of a gam me to make u us the exercisses. The rods are a suita ble means fo or our purpo oses becausee they are ha alfway betweeen a toyy and a tool for work. Teacching mathematics usingg colorful strrips was expposed in 1952 by George es Cuisenairee (1891‐1976 6), a teacherr of Belggian primary school, in hiis book "The numbers off colors" Its u use was deve eloped and ppopularized by the egypttian Cale eb Gattegno (1911‐1988 8), which applied this evven languagge teaching. In the systeem, there are a 10 stripss of squaare section o of 1x1 cm, wiith lengths ra anging from 1 cm to 10 ccm according g to a color ccode: Thro ough play with the rodss the child will w beco omes familiaar with the numbers firrst and then with h what th hey represe ent (lenggths, areass, volumess), while he unde erstand the way off the bassic operrations. The tabs of thiss book are to induce the me, through w which the ch hild in additio on gam to co olor code in rods system m, will learn to consstruct num merical se eries easily, mea asurements, decompose numbers, calcu ulating sumss and differe ences. He may also be initiatted at mo ore advance ed operrations such h as multiplication an nd divission calculaation, meaasurement of areaas and volum mes, sharingg amounts, or even n get to guesss the primee numbers and the P Pythagorean n theorem. It is therefore important you y do not to leave your child alone in fron nt of the boo ok, but you accomp pany with him an attitud de of play p across the problemss posed in the bookk and usingg the time spent s to solve our own questio ons on the reasons r for its behaavior, and w we encouragge you to try t alterrnative m methods or addition nal operrations to th hose proposeed in each tab whe en it have completed it successfully. Or even n lets be he who proposses them to us. Thus, in addition to ffacilitate learning as if itt were a gam me, we can aalso unde erstand how w a child's miind works an nd the strateegies he preffer to use to solve differeent problem ms. This will h help us to o know our sson and acco ompany him new challen ges of development. But to associatee enjoyment with learnin ng, it is interresting to reccord on the child's perceeption of this activity, evven m of study. TTo help this, h he has to fill each tab. ass at school. playing, is a form This wo ork is subject to the Atttribution‐ShareAlike 4.0 0 License Creative Com mmons International. TTo view a copy of this license, visit http://crea ativecommons.org/liceenses/by‐sa/4.0/deed.es_ES Translattion from the original SSpanish

Name: _______________________________________________________ Date: _________________________ Write into the box, as in the example, the number corresponding to each rod by color

Name: _______________________________________________________ Date: _________________________ Series: construct the following series with the rods, and write its number under the figures, as in the example 1 – 2 – 1 – 2– 1 – 2 – 1 – 2

‐

1 – 2 – 3 – 4 – 5

1 – 2 – 3 – 1 – 2 – 3

2 – 4 – 6

1 – 3 – 5 – 7

2 – 4 – 8

Name: _______________________________________________________ Date: _________________________ Write the result of the sums, and you will can see which it forms a series 1 + 1 = ________

2 + 1 = _________

3 + 1 = _________

4 + 1 = _________

5 + 1 = _________

6 + 1 = _________

7 + 1 = _________

Name: _______________________________________________________ Date: _________________________ Write double each rod and painting the result with its color, as in the example 1 + 1 = __2______

2 + 2 = _________

3 + 3 = _________

4 + 4 = _________

5 + 5 = _________

6 + 6 = _________

Name: _______________________________________________________ Date: _________________________ Expresses the following lengths rods in two different ways, and paint with its colors the solutions 6

Name: _______________________________________________________ Date: _________________________ Expresses the following lengths rods with in different ways and paint with its colors the solutions 7

Name: _______________________________________________________ Date: _________________________ Measure the length of the gray path indicated in each figure with the minimum number of rods L = _______

L = _______

Name: _______________________________________________________ Date: _________________________ Make a train of rods similar to each figure and determine its length L = _______

L = _______

Name: _______________________________________________________ Date: _________________________ Add together 2+1 = _____

3 + 2 = _____

2 + 2 = _____

4 + 1 = _____

4 + 2 = _____

3 + 5 = _____

5 + 2 = _____

4 + 3 = _____

Name: _______________________________________________________ Date: _________________________ Add together 7 + 1 = _____

8 + 2 = _____

7 + 3 = _____

4+4 = _____

4+5 = _____

3 + 6 = _____

2 + 7 = _____

8 + 1 = _____

Name: _______________________________________________________ Date: _________________________ Commutative Property: measure the path length in each figure of the several proposed forms. You will find it to be equal: write each solution and the total. L = ___________ ó ___________ = ________

L = ______________ ó _______________ ó _______________ = _________

Name: _______________________________________________________ Date: _________________________ Commutative Property: writing backwards 1 + 2 = _____

2 + 3 = _____

3 + 4 = _____

5 + 2 = _____

6 + 3 = _____

Name: _______________________________________________________ Date: _________________________ Decompose the number 10 in two terms, of all possible forms 10

5 + 5 = _____

6 + 4 = _____

7 + 3 = _____

8 + 2 = _____

9 + 1 = _____

Name: _______________________________________________________ Date: _________________________ Add together 4+5 = _____

3 + 4 = _____

2 + 6 = _____

5 + 1 = _____

1 + 2 + 3 = _____

3 + 3 + 3 = _____

3 + 2 + 2 = _____

4 + 4 + 4 = _____

Name: _______________________________________________________ Date: _________________________ Commutative Property: write in two different ways 1 + 2 + 1= ___________ ó ___________

2 + 3 + 2= ___________ ó ___________

3 + 4 + 3= ___________ ó __________

Name: _______________________________________________________ Date: _________________________ Decompose the number 12 in two terms, of all possible ways 12

5 + 7 = _____

6 + 6 = _____

10 + 2 = _____

8 + 4 = _____

9 + 3 = _____

Name: _______________________________________________________ Date: _________________________ Add together 4 + 4 + 1 = _____

3 + 1 + 2 = _____

2 + 2 + 3 = _____

2 + 2 + 1 = _____

1 + 2 + 4 = _____

4 + 3 + 2 = _____

2 + 3 + 2 = _____

3 + 3 + 2 = _____

Name: _______________________________________________________ Date: _________________________ Calculate the length of the gray path that it’s indicated in each figure L = _______

L = _______

Name: _______________________________________________________ Date: _________________________ Decompose the number using two or three addends, of all possible forms 3

2 + 1 = _____

1 + 1 + 1 = _____

3 + 3 = _____

4 + 2 = _____

5 + 1 = _____

2 + 2 + 2 = _____

Name: _______________________________________________________ Date: _________________________ Decompose the number using three summands, of all possible forms 4

2 + 1 + 1 = _____

3 + 3 + 2 = _____

4 + 2 + 2 = _____

5 + 1 + 2 = _____

6 + 1 + 1 = _____

Name: _______________________________________________________ Date: _________________________ Remove to the upper’s rod value, the second rod value (in the down line): the remains is subtraction. Make the subtraction with the rods and write as in the example. Example:

3 ‐ 2 = 1

Name: _______________________________________________________ Date: _________________________ Subtract, completing the missing length with a rod, and write the result 3 ‐ 2 = _____

3 ‐1 = _____

4 ‐ 3 = _____

5 2 = _____

6 ‐ 3 = _____

Name: _______________________________________________________ Date: _________________________ Add several times to multiplying 1 + 1 = 1 add twice = 1 x 2 = _____

2 + 2 = 2 add twice = 2 x 2 _____

2 + 2 + 2 = 2 add three times = 2 x3 = _____

2 + 2 + 2 + 2 = 2 add four times = 2 x4 = _____

3 + 3 = 3 add twice = 3 x 2 = _____

3 + 3 + 3 = 3 add three times = 3 x 3 = _____

1 + 1 + 1 = 1 add three times = 1 x 3 = _____

Name: _______________________________________________________ Date: _________________________ Multiply ....it is made figures! The result is the surface of those figures. You try it using the 2 rod. 2x1 = _____

2x2 = _____

2x3 = _____

2x4 = _____

2x5 = _____

3x2 = _____

3 x 3 = _____

3 x 4 = _____

Name: _______________________________________________________ Date: _________________________ Areas: forming the proposed squares, and make it too with a different form, painting your solution. L = 2

L = 3

L = 4

Name: _______________________________________________________ Date: _________________________ Areas: Make squares (they are figures with four equal sides) using rods. The surface is the sum of all rods used in one square. Write the surface (sum of rods).

Side = 1, Surface = ____ Side = 2, Surface = ____

Side = 3, Surface = ____

Side = 4, Surface = ____

Side = 5, Surface = ____

Name: _______________________________________________________ Date: _________________________ Areas: calculate the area of a rectangle (like a square "extended" because it has four sides equal in pairs), with the dimensions indicated by the numbers, joining the rods you need to form the figures: 2 x 1 = ____

3 x 2 = ____

2 x 3= ____

3 x 4= ____

5 x 2= ____

4 x 2= ____

Name: _______________________________________________________ Date: _________________________ Calculate the surfaces of these irregular figures (because the sides are not equal). You can place rods to form them and add up its values. You can also check the solution by counting squares containing. Surface = __________

Surface = __________

Surface = ___________

Name: _______________________________________________________ Date: _________________________ Areas: decomposing these surfaces as the sum of the other two rods indicated. Example: 5 x 2 = 3 x 2 + 2 x 2

5 x 3= 3 x 3 + 2 x 3

3 x 4= 3 x 2 + 2 x 3

6 x 2= 2 x 2 + 2 x 2 + 2 x 2

6 x 2= 3 x 2 + 3 x 2

Name: _______________________________________________________ Date: _________________________ Cut out the following figures. You will need it in the next tabs

Name: _______________________________________________________ Date: _________________________ Calculate the area of the rectangle. If we divided in half two squares, how measure the area of each square? You can help the cutouts for checking, further with the rods. Rectangle = 4 x 2= ________

1 Square = 2 x 2 = ________

Rectangle = 6 x 3= ________

1 Square = 3 x 3 = ________

Rectangle = 8 x 4= ________

1 Square = 4 x 4 = ________

Name: _______________________________________________________ Date: _________________________ Calculate the area of the square. If it splits in half in two equal right triangles, how measure the area of each triangle? (The two together must be equal to the surface of the square) You can help of the cutouts to check, in addition to the rods, squares and square or by counting (included they are divided by the diagonal line). Square = 4 x 4 = __________ Triangle = Square / 2 = ________

Square = 6 x 6 = __________ Triangle = Square / 2 = ________

Name: _______________________________________________________ Date: _________________________ Construct the right triangle and calculate the length of the missing side in the figure (its length). You can help the cutouts to check, or by seeking the rod to close the triangle. L = __________

Solution

Name: _______________________________________________________ Date: _________________________ Finding prime numbers: colored with the same color in the first rod (the first in each question), the P letter when these number can only be decomposed into 1 rods (it is a prime number), whitout any intermediate decompositions. 2

Name: _______________________________________________________ Date: _________________________ Finding prime numbers: colored with the same color in the first rod (in each question), the P letter when these number can only be decomposed into 1 rods (it is a prime number), whitout any intermediate decompositions. 7

Name: _______________________________________________________ Date: _________________________ Imagine that the first rod of each account is the number of sweets we have, and must be distributed between two children. Use the rods to divide by two (half) and write the result: 2 / 2 = _____

4 / 2 = _____

6 / 2 = _____

8 / 2 = _____

10 / 2 = _____

Name: _______________________________________________________ Date: _________________________ Divide each number indicating the first rod (dividend) between the divisor (the second rod number) and write the result (the result is the number of second rods you need). 3 / 3 = _____

3 / 1= _____

6 / 2 = _____

6 / 3 = _____

6 / 1 = _____

Name: _______________________________________________________ Date: _________________________ Divide each amount of the dividend between the quotient, writing the result (number of equal rods that you had to use) and the rest (value of the last rod that you had to add to the quotient to complete the dividend). Example: 6 / 5 = __1___ Remainder: __1___

Dividend

Divisor

Remainder

6 / 2 = ______ Remainder: ______

Dividend

Divisor

Remainder

7 / 3 = _____ Remainder: ______

Dividend

Divisor

Remainder

8 / 3 = _____ Remainder: ______

Dividend

Divisor

Remainder

Name: _______________________________________________________ Date: _________________________ Volumes: Build, by stacking white, yellow and green rods, the following 3D figures (with volume), by using only one type of rods for each figure. 1 4 8 9 18 27 40