diarios de matemáticas - K-5MathTeachingResources.com

Transcripción

MP
SA
DIARIOS DE
MATEMÁTICAS
LE
de 5º Grado
5th Grade Math Journals contains 90 math journal tasks
aligned with the Common Core State Standards. All tasks are
based on a problem solving approach and provide valuable
opportunities for students to organize, clarify and reflect on
their thinking while developing key mathematical skills and
understandings.
www.k-5mathteachingresources.com
Contents
1. What are Math Journals? .................................................................................. ....... 1-6
2. Overview of Tasks .................................................................................................. 7-12
3. Math Journal Task Labels .................................................................................. 13-102
4. Resources .............................................................................. ............................. 103-109
 Coordinate Grid Paper (Tasks 7, 8, 9, and 85)
 Cm Grid Paper (Task 55)
 Triangles Pack (Tasks 87 and 88)
 Geoboard Paper 5x5 and 7x7 (Task 89)
SA
5. Math Rubric Samples ........................................................................................ 110-119
- Sample 1 Student Copy
- Sample 2 Student Copy
MP
- Sample 1 Classroom Display Copy
- Sample 2 Classroom Display Copy
LE
6. User License ....................................................................................................... 120-121
What Are Math Journals?
A math journal, or problem solving notebook as they are sometimes referred to, is a book in
which students record their math work and thinking. Math journals can be used to:
 Record the solutions to math problems: When solving problems in a math journal,
students are expected to record their strategy and thought processes, as well as
solutions.
 Write about learning: At times students may be asked to reflect on their math learning.
For example, students may be asked to write about "what you already know about ......" at
the beginning of a unit, or "what you did today, what you learned, and any questions you
have", or "the three most important things you learned in this unit and why."
By dating entries a math journal provides a chronological record of the development of a
student’s mathematical thinking throughout the year.
SA
Why Use Math Journals?
LE
MP
While students learn how to "do" math, they must also learn how to articulate what they are
learning. It is important to provide many opportunities for students to organize and record
their work without the structure of a worksheet. Math journals support learning because, in
order to get their ideas on paper, students must organize, clarify, and reflect on their thinking.
Initially many students will need support and encouragement in order to communicate their
ideas and thinking clearly on paper but, as with any skill, the more they practice the easier it
will become.
Math Journals also serve as invaluable assessment resources that can inform classroom
instruction. Requiring students to communicate their reasoning processes provides a useful
insight into what a child understands, how s/he approaches ideas and what misconceptions s/he
has.
What Are The Characteristics of a Good Math Journal Question?
A Good Math Journal Question ….
 builds in differentiation by allowing for multiple entry points, strategies, and recording
techniques thereby allowing all students to work at their individual level of thinking,

provides the opportunity for students to learn by moving beyond what they already know
when answering a question, and the teacher to learn about each student from the
1
attempt,
 may have more than one solution or a variety of possible solution paths that range from
simple to complex,
 requires more than just remembering a fact or reproducing a skill,
 provides opportunities for students to represent their mathematical ideas using models
and written language,
 provides opportunities for students to justify their reasoning and evaluate the reasoning
of others,
 has clear, concise directions.
How Are Math Journal Sessions Structured?
LE
MP
SA
The most important thing to consider when developing a math journal question is whether the
question involves significant mathematics. Closed questions such as, “There are two bowls of
apples. Each bowl has eight apples. How many apples in all?” do little to develop mathematical
thinking if the student can answer the question before even getting back to her seat. The
student may spend 15 minutes drawing and coloring apples but the math thinking is limited.
Changing the question from a closed to an open format such as, “There are 16 apples to put into
bowls. Each bowl must have the same number of apples. Show as many different solutions as you
can.” creates greater potential to stimulate mathematical thinking and reasoning.
A variety of math journal tasks have been included in this E-book. Some tasks can be used as
quick warm up tasks. Others are suitable for independent practice or group work, as a ThinkPair Share, or as homework or assessment tasks. More involved tasks can be as used as the
main task during the math block.
When used as the main task during the math block the math journal session would typically
consist of three main components: before, during and after. During the before phase, or minilesson, the role of the teacher is to mentally prepare students for the task, ensure that
students understand the task and establish expectations. In order to prepare students for the
task some teachers like to model a similar problem, in a large class math journal while others
prefer to pose the task right away and then have students brainstorm a list of possible solution
strategies. If you do decide to model a task it is important that you take care not to undermine
students' thought processes by telling them what to do, or by discouraging them from making
sense of alternative strategies or solutions. To ensure that students understand a task the
teacher may discuss certain vocabulary involved in the task or have students explain what the
problem is asking in their own words. Establishing expectations from the outset for math
journal sessions is crucial. Asking students to record their thinking on paper using diagrams,
2
numbers, or words places an emphasis on process, indicating to students that their thinking is as
important as the answers.
In the during, or Student Activity stage, encourage students to use their own ideas. Different
strategies and recording methods should be valued. This is a time for the teacher to listen and
find out how students are approaching a problem. The teacher may confer with individuals or
small groups of students and record anecdotal notes, or use questioning to guide students
needing extra support.
I agree with ___ because ……
I disagree with ___ because ……
I also noticed ……
I’d like to build on what …. said ……
I didn’t understand ……
I think what …... meant is ……
I predict that …..
My strategy was …...
I think a more efficient strategy would be ....
Another possible strategy would be ...
Can you say more about … ...?
Why do you think that?
How do you know that?
Can you explain that in another way?
Can you prove that?
LE
MP
SA
The after phase, or Share component, is a crucial component of the math journal session where
academic talk between, and among, students is promoted. Several students may be selected to
share their solutions and justify their reasoning. Selecting students who have used different
strategies, models, or recording styles will provide models for other students of possible new
approaches to try at another time. The teacher's role in creating an environment where
students come ready to think, listen, share, and evaluate both their own and the reasoning of
their peers is critical. Building this environment takes time, patience, and consistency.
Strategies such as moving to a specific location in the classroom to gather for the share, using
appropriate wait time after asking a question, accepting all ideas and answers regardless of
obvious errors, and having students share their work with a partner before the whole class
Share all encourage student communication. Early in the year a chart of Math Talk stems can
provide a useful support to scaffold students' interactions during the Share. Possible stems
include:
Can Math Journal Tasks Be Revisited During The Year?
Repeating, or revisiting tasks, allows students to engage with tasks at a deeper level. On the
first occasion the student may be focused on ‘how to do’ the task. Subsequent visits provide an
opportunity for students to communicate their reasoning more clearly. Making slight variations
3
to an open ended task or changing the materials used to complete a task helps to maintain
interest while providing time for students to further develop skills and concepts. For example, a
question such as, ‘Which is larger, 2.9 or 2.13? Explain your reasoning' can be revisited many
times during the course of the year by simply changing the decimals. Similarly, 'You divide two
numbers and the quotient is 2.5. What might the two numbers be?' can be revisited by changing
the problem to 'You multiply two numbers and the product is .....'
You may decide to provide opportunities for students to revisit tasks by introducing math
journal tasks to the whole class and then placing similar tasks in centers for students to revisit
at other times during the year. Another option is to choose one journal task and repeat it
several times throughout the year, with slight variations, as a record of the development of
math skills and understandings for student portfolios.
How Often Should I Use Math Journals in My Class?
MP
SA
This is entirely up to the individual teacher. Some teachers use them several times a week.
Other teachers who have more restrictions on their math sessions due to using a mandated
curriculum set aside one session per week for math journals and then select a journal task that
correlates with the current unit of study. You may choose to use some tasks as quick warm ups,
or as homework or assessment tasks. The important thing is to ensure that students are being
given regular opportunities throughout the year to record their mathematical thinking in a way
which makes sense to them.
LE
What Type Of Book Should My Students Use As A Math Journal?
At the K-5 level many teachers use a blank notebook as the math journal so that students are
not restricted by lines and have the space to choose whether to use diagrams, numbers, words
or a combination of these to record their thinking.
Content: This E-book contains 90 math journal tasks. Content for all tasks is aligned with the
Common Core State Standards. See the provided tables for an outline of the focus domain and
Common Core Standard for each task.
In addition to the standards that describe content, there are eight Common Core State
Standards focusing on mathematical practice, which are implicit in many of the math journal
tasks in this E-book. These are:
Mathematical Practices:
1. Make sense of problems and persevere in solving them.
2. Reason abstractly and quantitatively.
3. Construct viable arguments and critique the reasoning of others.
4. Model with mathematics.
4
5. Use appropriate tools strategically.
6. Attend to precision.
7. Look for and make use of structure.
8. Look for and express regularity in repeated reasoning.
Different mathematical practices will be brought out in different tasks, depending on how the
teacher presents the tasks and approaches student responses. For example, the open-ended
nature of these tasks require students to make sense of the question before they select a
strategy to solve the problem. This will be supported by skillful teaching moves but can be
undermined if the teacher removes the demand for student sense making by telling students
how to solve a problem, or expecting all students to solve the problem in the same way.
Math Rubric
LE
MP
SA
Many of the tasks require that students use a mathematical model (drawings, charts, graphs,
equations etc.) and/or construct viable arguments by explaining their thinking and justifying
their conclusions. Other tasks require students to reason abstractly and quantitatively by
attending to the meaning of quantities, not just how to compute them, and knowing and flexibly
using different properties of operations. Some tasks encourage students to look closely to
discern patterns, structures and mathematical relationships. Students should be expected to
attend to precision by communicating precisely using mathematical language and carefully
formulated explanations. If students are given the opportunity to share their solutions and
strategies at the conclusion of the math journal session opportunities arise to critique the
reasoning of others. Allowing students to make their own decisions as to which mathematical
tools are appropriate for a given situation is also important. The teacher's role is to ensure that
a variety of tools and recording paper are available should students choose to use them, rather
than telling students which tools to use for a given task.
A rubric can be a powerful tool for both teaching and assessment. Use of a rubric can improve
student performance, as well as monitor it, by making teachers' expectations clear and by
showing students how to meet these expectations. The result is often marked improvements in
the quality of student work and in learning. Two sample Math Rubrics, suitable for use with
math journal tasks, are included in this E-Book. You may like to choose one to use with your
class or use them as a model to design your own. Make an enlarged copy for display in the
classroom and have students paste a smaller copy inside the front cover of their math journal
for easy reference.
5
Printing the Tasks:
The 90 math journal tasks are formatted so that you can print them on mailing labels (Avery
Standard, 5160). Just print and pass out for students to peel and stick at the top of their
math journal page. If you experience any difficulty printing the labels try the following:
1. Verify that you have a current version of Adobe Acrobat Reader. To
determine the version of Adobe Acrobat, open Adobe from your desktop or
start menu, click on help, and then About Acrobat Reader. Download an
update to your reader from the Adobe Reader download page on Adobe's
website.
2. When in the Preview Labels screen click the Print icon.
3. Under Page Handling make sure Page Scaling is set to None and AutoRotate and Center is not selected.
4. Click OK.
MP
SA
Placing the labels in student journals provides information for parents, teachers and
administrators as to what task the student was working on. The Avery Standard 5160
label is used in order to give students as much blank space on the page as possible to
record their thinking. Teachers may find it useful to write each task on a chart or
whiteboard before introducing it so that students see the task in large print before
beginning work.
Resources
Resources have been included for use with the following math journal tasks:
LE

Coordinate Grid Paper (Tasks 7, 8, 9, and 85)

Cm Grid Paper (Task 55)

Triangles Pack (Tasks 87 and 88)

Geoboard Paper 5x5 and 7x7 (Task 89)
In addition, our website offers a wide range of free math center task cards and resources
suitable for use in 5th Grade classrooms. Please see the links below as a starting point.
http://www.k-5mathteachingresources.com/5th-grade-number-activities.html
http://www.k-5mathteachingresources.com/5th-grade-geometry.html
http://www.k-5mathteachingresources.com/5th-grade-measurement-and-data.html
6
Tarea
31
Esfera
Estándar
Diario de Tareas Matemáticas
(use Bookmarks tab to navigate to label pages)
Un agricultor cultiva 196kg de zanahorias. Se las vende a un tendero que las divide en bolsas de 5kg y 2 kg. Si el
tendero utiliza el mismo número de bolsas de 2kg y 5kg, ¿cuántos de cada una utilizo? Explica tu forma de pensar.
32
5.NBT7
Muestra 5 soluciones posibles para cada declaración: a) la suma de 2 decimales es menor que 1 b) la suma de 2
decimales es igual a 1 c) la suma de 2 decimales es mayor que 1.
33
5.NBT7
Muestra 5 soluciones posibles para cada declaración: a) la diferencia entre 2 decimales es menor que 1
b) del diferencia entre 2 decimales es igual a 1 c) la diferencia entre 2 decimales es mayor que 1.
34
5.NBT7
La diferencia entre dos decimales es 6.53. ¿Cuáles podrían ser los dos decimales? Muestra 5 soluciones diferentes.
35
5.NBT7
Crea y resuelve un problema de palabras con un cociente de 3.4. ¿Cómo eligiste los números?
36
5.NBT7
Multipliqué dos números y tengo un producto más pequeño que los dos factores. ¿Cuáles podrían ser los dos números?
37
5.NBT7
Crea un problema de palabras que involucre la multiplicación de decimales en los cuales aparezcan los números 3, 5, 7
y 2. Muestra cómo resolvería el problema.
38
5.NBT7
Gaste $156 para encerrar mi jardín con un costo de $6.50 por yarda para la esgrima. Dibuja dos planes posibles para
mi jardín. Explica tu razonamiento.
MP
39
SA
5.NBT6
Numero y
Operaciones
de Valor
Posicional
1/a-1/b=1/c
¿Cuántos diferentes conjuntos de números puedes encontrar que hagan esta oración verdadera?
40
5.NF2
Crea un problema de palabras que se pueda resolver al restar dos fracciones con denominadores distintos. Explica
cómo puedes utilizar fracciones equivalentes para ayudarte a resolver el problema.
41
5.NF2
Dos fracciones se suman y dan un resultado de 2/4. ¿Cuáles podrían ser las dos fracciones? Muestra al menos 5
soluciones.
42
5.NF2
La suma de dos números mixtos con denominadores distintos es de 5 8/10. ¿Cuáles podrían ser los dos números
mixtos?
43
5.NF2
La diferencia entre dos números mixtos con denominadores distintos es 3¾ ¿Cuáles podrían ser los dos números mixtos?
44
5.NF2
El peso total de tres paquetes es ⅞lb. Un paquete pesa ¼lb. ¿Cual podría ser el peso de los otros dos paquetes?
45
5.NF2
2/5 de los animales en una tienda de mascotas son perros y 3/8 son gatos. El resto de los animales son pájaros o
ratones. ¿Qué fracción de todos los animales son perros o gatos? ¿Qué fracción de todos los animales no son perros
ni gatos? Explica.
LE
5.NF1
Numero y
Operaciones:
Fracciones
9
La diferencia entre dos decimales
es 6.53. ¿Cuáles podrían ser los dos
decimales? Muestra 5 soluciones
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
SA
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
diferentes.
LE
MP
diferentes.
46
Crea y resuelve un problema de
palabras con un cociente de 3.4.
¿Cómo eligiste los números?
SA
MP
LE
47
Multipliqué dos números y tengo un
producto más pequeño que los dos
factores. ¿Cuáles podrían ser los
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
SA
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
dos números?
LE
MP
dos números?
48
Crea un problema de palabras que
involucre la multiplicación de decimales en
los cuales aparezcan los números 3, 5, 7 y
2. Muestra cómo resolvería el problema.
SA
LE
MP
49
Gaste $156 para encerrar mi jardín con
un costo de $6.50 por yarda para la
esgrima. Dibuja dos planes posibles
para mi jardín. Explica tu razonamiento.
SA
LE
MP
50
1/a-1/b=1/c
¿Cuántos diferentes conjuntos de
números puedes encontrar que
hagan esta oración verdadera?
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
SA
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
1/a-1/b=1/c
LE
MP
1/a-1/b=1/c
51
Crea un problema de palabras que se pueda
resolver al restar dos fracciones con
denominadores distintos. Explica cómo
puedes utilizar fracciones equivalentes para
ayudarte a resolver el problema.
SA
LE
MP
52
Mi trabajo muestra que tengo un profundo entendimiento de las matemáticas en esta tarea

Resolví el problema correctamente usando una estrategia eficiente.

Mi explicación está muy clara y lógica. Usé vocabulario matemático efectivamente.

Incluí evidencias que comprueban que mi trabajo está exacto.
Mi trabajo muestra que tengo un buen entendimiento de las matemáticas en esta tarea
SA

Resolví el problema correctamente usando una estrategia apropiada.

Mi explicación está razonablemente clara. Usé algunas palabras de vocabulario matemático.
MP
Mi trabajo muestra algún entendimiento de las matemáticas en esta tarea
LE

Resolví parte del problema correctamente o cometí algunos pequeños errores. Usé una estrategia que
fue parcialmente útil, pero no llegue a una solución correcta.

Algunas partes de la explicación no están claras. Usé muy pocas palabras de vocabulario matemático.
Mi trabajo muestra que necesito más ayuda para entender las matemáticas en esta tarea

No di ninguna respuesta o la respuesta está incorrecta. Mi estrategia es inadecuada.

No incluí una explicación o mi explicación es confusa o irrelevante.
Mi trabajo muestra que tengo un profundo entendimiento de las matemáticas en esta tarea

Resolví el problema correctamente usando una estrategia eficiente.

Modelé el problema usando un dibujo o diagrama muy claro, una tabla, un gráfico, o una ecuación.

Mi explicación está muy clara y exacta. Usé vocabulario matemático preciso, apoyé mis predicciones
y conclusiones con pruebas y evalué la razonabilidad de mi solución.
Mi trabajo muestra que tengo un buen entendimiento de las matemáticas en esta tarea
Resolví el problema correctamente usando una estrategia apropiada.

Modelé el problema usando un dibujo o diagrama claro, una tabla, un gráfico, o una ecuación.

Mi explicación está razonablemente clara y exacta. Usé algunas palabras de vocabulario matemático,
apoyé mis predicciones y conclusiones con pruebas y evalué la razonabilidad de mi solución.
LE
MP
SA

Mi trabajo muestra algún entendimiento de las matemáticas en esta tarea

Resolví parte del problema correctamente o cometí algunos pequeños errores. Usé una estrategia
que fue parcialmente útil, pero no llegue a una solución correcta.

Intenté modelar el problema usando un dibujo o diagrama, una tabla, un gráfico, o una ecuación.

Algunas partes de mi explicación están clara. Trate de usar algunas de las palabras de vocabulario
matemático e intenté de apoyar mis descripciones y conclusiones con pruebas.
que
necesito
más ayuda
entender
las matemáticas en esta tarea
Mi trabajo
I did notmuestra
solve the
problem
correctly
or I didpara
not finish
my work.

No di ninguna respuesta o di una respuesta incorrecta. Mi estrategia era inapropiada.

No modelé el problema usando un dibujo o diagrama, una tabla, un gráfico, o una ecuación.

No incluí una explicación o mi explicación es confusa o irrelevante.

diarios de matemáticas - K-5MathTeachingResources.com

Transcripción

Documentos relacionados

Estándares Curriculares para Matemáticas