Download - Maths with rods
![Page 1: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/1.jpg)
Pla
2013
ay and
3
Learn
440 ex
Mercise
athe tabs
hs ws to p
Jos
witplay w
M
sé Mª de
h rwith p
María Alo
e Cuenca
odsarent
nso Garc
de la Cr
s ts
cía
ruz
![Page 2: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/2.jpg)
Ma
Intro
This wheand you ther
Withbetwgama toy
TeacBelgCalesqua
Throbecoand (lengundeoper
The gamto coconsmeacalcualso operdivisareaeventhe P
It isleavbut of pbookour behaalteroperwheevenundeus to
But play
This wo
Translat
ths with r
oduction
book beginen they compfor us, theirdo this at e
refore they m
h the activitiween the mome to make uy and a tool
ching mathegian primary eb Gattegno are section o
ough play womes familiathen with
gths, areaserstand thrations.
tabs of thisme, through wolor code in struct numasurements, ulating sumsbe initiat
rations suchsion calculaas and volumn get to guesPythagorean
therefore e your child you accomp
play across tk and usingown questioavior, and wrnative mrations to then it have con lets be he erstand howo know our s
to associateing, is a form
ork is subject to the Att
tion from the original S
rods
s a collectioplete their scr parents. Thearly stage omay reach th
ies of this fironths of Octus the exercisfor work.
matics usingschool, in hi(1911‐1988
of 1x1 cm, wi
ith the rodsar with the h what ths, volumese way of
s book are which the chrods systemmerical se
decompos and differeted at moh as multiation, meames, sharingss the primen theorem.
important yalone in fronpany with hihe problemsg the time sons on the rwe encouragmethods ohose proposempleted it swho propos
w a child's mison and acco
e enjoyment m of study. T
tribution‐ShareAlike 4.0
Spanish
on that is intchool day orhe enjoymenof his life, yeir full intell
rst issue willober and Noses. The rod
g colorful stris book "The8), which apith lengths ra
s the child wnumbers fir
hey represes), while f the bas
to induce thild in additiom, will learn eries easise numbeences. He more advanceplication anasurement g amounts, e numbers a
you do not nt of the boom an attituds posed in tspent to solreasons for ge you to tr additioned in each tuccessfully. ses them to ind works anompany him
with learninTo help this, h
0 License Creative Com
ended to her they have ant of the actyou will increlectual deve
l facilitate thovember. Ths are a suita
rips was exp numbers ofplied this evanging from
will rst ent he sic
he on to ly, rs, ay ed nd of or nd
to ok, de he ve its try nal ab Or us. Thus, in nd the stratenew challen
ng, it is interhe has to fill
mmons International. T
ii
elp those cha holiday. It tivities is essease the effelopment.
he developmhey are baseble means fo
posed in 195f colors" Its uven languag1 cm to 10 c
addition to fegies he prefges of devel
resting to rec each tab. as
To view a copy of this l
ildren who eis essential tential for chfort they to
ment of the bd on the useor our purpo
2 by Georgeuse was devege teaching. cm according
facilitate leafer to use toopment.
cord on thes at school.
icense, visit http://crea
enjoy workinto use this shildren to debe able to
basic math se of rods, so oses because
es Cuisenaireeloped and pIn the syste
g to a color c
rning as if it solve differe
child's perce
ativecommons.org/lice
ng "a little mshared time evelop a loveapply it in t
skills at starto we'll have te they are ha
e (1891‐1976popularized em, there acode:
t were a gament problem
eption of th
enses/by‐sa/4.0/deed.
more" at homnicely for the of learningthe future, a
t of the schoto get hold oalfway betwe
6), a teacherby the egyptare 10 strips
me, we can ams. This will h
is activity, ev
es_ES
me, hem g. If and
ool, of a een
r of tian s of
also help
ven
![Page 3: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/3.jpg)
1
Name: _______________________________________________________ Date: _________________________
Write into the box, as in the example, the number corresponding to each rod by color
3
![Page 4: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/4.jpg)
2
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 ‐ 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
![Page 5: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/5.jpg)
3
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 = _________
![Page 6: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/6.jpg)
4
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 = _________
![Page 7: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/7.jpg)
5
Name: _______________________________________________________ Date: _________________________
Expresses the following lengths rods in two different ways, and paint with its colors the solutions
6
5
10
9
4
8
![Page 8: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/8.jpg)
6
Name: _______________________________________________________ Date: _________________________
Expresses the following lengths rods with in different ways and paint with its colors the solutions
7
12
17
11
14
15
![Page 9: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/9.jpg)
7
Name: _______________________________________________________ Date: _________________________
Measure the length of the gray path indicated in each figure with the minimum number of rods
L = _______
L = _______
L = _______
![Page 10: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/10.jpg)
8
Name: _______________________________________________________ Date: _________________________
Make a train of rods similar to each figure and determine its length
L = _______
L = _______
L = _______
L = _______
![Page 11: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/11.jpg)
9
Name: _______________________________________________________ Date: _________________________
Add together
2+1 = _____
3 + 2 = _____
2 + 2 = _____
4 + 1 = _____
4 + 2 = _____
3 + 5 = _____
5 + 2 = _____
4 + 3 = _____
![Page 12: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/12.jpg)
10
Name: _______________________________________________________ Date: _________________________
Add together
7 + 1 = _____
8 + 2 = _____
7 + 3 = _____
4+4 = _____
4+5 = _____
3 + 6 = _____
2 + 7 = _____
8 + 1 = _____
![Page 13: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/13.jpg)
11
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 _______________ = _________
![Page 14: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/14.jpg)
12
Name: _______________________________________________________ Date: _________________________
Commutative Property: writing backwards
1 + 2 = _____
2 + 3 = _____
3 + 4 = _____
5 + 2 = _____
6 + 3 = _____
![Page 15: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/15.jpg)
13
Name: _______________________________________________________ Date: _________________________
Decompose the number 10 in two terms, of all possible forms
10
5 + 5 = _____
6 + 4 = _____
7 + 3 = _____
8 + 2 = _____
9 + 1 = _____
![Page 16: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/16.jpg)
14
Name: _______________________________________________________ Date: _________________________
Add together
4+5 = _____
3 + 4 = _____
2 + 6 = _____
5 + 1 = _____
1 + 2 + 3 = _____
3 + 3 + 3 = _____
3 + 2 + 2 = _____
4 + 4 + 4 = _____
![Page 17: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/17.jpg)
15
Name: _______________________________________________________ Date: _________________________
Commutative Property: write in two different ways
1 + 2 + 1= ___________ ó ___________
2 + 3 + 2= ___________ ó ___________
3 + 4 + 3= ___________ ó __________
![Page 18: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/18.jpg)
16
Name: _______________________________________________________ Date: _________________________
Decompose the number 12 in two terms, of all possible ways
12
5 + 7 = _____
6 + 6 = _____
10 + 2 = _____
8 + 4 = _____
9 + 3 = _____
![Page 19: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/19.jpg)
17
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 = _____
![Page 20: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/20.jpg)
18
Name: _______________________________________________________ Date: _________________________
Calculate the length of the gray path that it’s indicated in each figure
L = _______
L = _______
L = _______
![Page 21: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/21.jpg)
19
Name: _______________________________________________________ Date: _________________________
Decompose the number using two or three addends, of all possible forms
3
2 + 1 = _____
1 + 1 + 1 = _____
6
3 + 3 = _____
4 + 2 = _____
5 + 1 = _____
2 + 2 + 2 = _____
![Page 22: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/22.jpg)
20
Name: _______________________________________________________ Date: _________________________
Decompose the number using three summands, of all possible forms
4
2 + 1 + 1 = _____
8
3 + 3 + 2 = _____
4 + 2 + 2 = _____
5 + 1 + 2 = _____
6 + 1 + 1 = _____
![Page 23: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/23.jpg)
21
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
![Page 24: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/24.jpg)
22
Name: _______________________________________________________ Date: _________________________
Subtract, completing the missing length with a rod, and write the result
3 ‐ 2 = _____
3 ‐1 = _____
4 ‐ 3 = _____
5 2 = _____
6 ‐ 3 = _____
![Page 25: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/25.jpg)
23
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 = _____
![Page 26: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/26.jpg)
24
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 = _____
![Page 27: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/27.jpg)
25
Name: _______________________________________________________ Date: _________________________
Multiply ....it is made figures! The result is the surface of those figures. You try it using the 3 rod.
3x1 = _____
3x2 = _____
3 x 3 = _____
3 x 4 = _____
![Page 28: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/28.jpg)
26
Name: _______________________________________________________ Date: _________________________
Areas: forming the proposed squares, and make it too with a different form, painting your solution.
L = 2
L = 3
L = 4
![Page 29: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/29.jpg)
27
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 = ____
![Page 30: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/30.jpg)
28
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= ____
![Page 31: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/31.jpg)
29
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 = ___________
Surface = ___________
![Page 32: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/32.jpg)
30
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
![Page 33: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/33.jpg)
31
Name: _______________________________________________________ Date: _________________________
Cut out the following figures. You will need it in the next tabs
![Page 34: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/34.jpg)
32
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 = ________
![Page 35: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/35.jpg)
33
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 = ________
![Page 36: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/36.jpg)
34
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
![Page 37: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/37.jpg)
35
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
3
4
5
6
![Page 38: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/38.jpg)
36
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
8
9
10
![Page 39: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/39.jpg)
37
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 = _____
![Page 40: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/40.jpg)
38
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 = _____
![Page 41: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/41.jpg)
39
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
![Page 42: Maths with rods](https://reader031.vdocuments.us/reader031/viewer/2022020118/568ca9321a28ab186d9c7b51/html5/thumbnails/42.jpg)
40
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