Workshop # 3

Workshop # 3

Geometry : Castles and Shadows

The opening activity silhouettes showed the relationship between 3 dimensional objects and two dimensional objects . It is a great way to show the relationship between three dimensional objects (cylinders, cubes and pyramids) and two dimensional shapes. There are students who will refer to a cube as a square and a rectangular prism as a rectangle. This activity will certainly help students who are  having difficulty with these concepts.
I did not use the exact activity for folding nets presented in this workshop; however, I have used nets in a geometry lesson. In the lesson, the students used nets to make the different shapes. The students selected the correct net for each shape and then made the shape. I feel the lesson in the workshop takes the concept a step further and encourages the students to use higher level thinking skills.
I have never used the activity Design Your Own Instruction. However, I was very impressed with the 5^th grade students 3 D representation. He used a special type of grid which made 3 D objects appear more realistic. We were able to see his details more clearly, even on a television monitor. I would be interested to see his instructions for the toy. Obviously, this type of activity includes many NCTM standards and touches on many connections with other subjects. This is a great lesson for any intermediate teacher.
There were many important issues in Mr. Ramirez's classroom. I substitute in 3 schools which have large Hispanic populations. Greenville County has a significant Hispanic population. I have worked in several primary classroom where the instructor does not correct spelling errors . When this is done in language arts especially with writing journals I feel that it is appropriate. If I know that a teacher uses this technique, I follow it. Most of the kindergarten classrooms that I have worked in use this technique.
In Mr. Ramirez's classroom he spent a long time defining the word "side". When defining and describing geometric shapes such as  the face (by this I mean the flat surfaces of solid figures or space figures), the students should be given clear definitions. I use visuals (smart boards/promethean boards), posters, geometric shapes, figures in textbooks, a shoe box, a ball ). And I provide very specific definitions before the activity begins. If a student needs extra guidance, I attempt to allow them to use inductive reasoning as well as assistance from their peers who may have solved the problem correctly. Sometimes, it is difficult for a substitute to prepare all of the necessary materials on short notice.
Finally, the drawing activity with the kindergarten students using shapes to make different objects is one I have used before. I have used activities where students use circles, rectangles, squares, triangles to make scarecrows, boys, boats etc. I feel that the activity which asks kindergarten students to draw three dimensional objects shows the difficulty which kindergarten students have with that type of visualization. It also helps us to think of age appropriate activities and how we can modify these activities for different age groups.
Activities That I Will Incorporate Into My Lessons
I will incorporate the concept of identifying shapes into my lessons. I will design a lesson for kindergarten students which allows them to explore shapes. The students will take a walk around the school, or school yard and look for objects identifying circles, triangles, squares or rectangles. When the students return to the classrooms the students will identify the object they saw and draw it using circles, triangles, squares or rectangles.
I will incorporate the concept of solid geometric figures into my lessons for a first grade class. The students will be shown the following forms: sphere, cone, cube and cylinder. I will show the students a mystery bag with objects inside which are shaped like the geometric solids. Students will take turns secretly selecting objects from the bag and then describing the objects to their classmates. "It is shaped like a cylinder." It can be made from plastic or paper. "What is it?" The answer is a cup.

 

Workshop #2 –Elementary Math Course

 

 

The second workshop ( Data: Posing Answers and Finding Questions) is very relevant to my daily experiences as a certified teacher substitute. When I receive "emergency calls" for a substitute, I have lessons and materials for grades K5-5. I need materials for all grade levels so this type of workshop is helpful for me. The discussion of age-appropriate activities for each grade levels is very helpful for me. I have found that in general k5 students are learning to represent quantities with symbols. Therefore, when I work with kindergarten students they are usually using pictographs or in some instances concrete graphs. Concrete graphing is important with kindergarten students because they compare concrete objects (real objects in the classroom) and are then able to move to abstract ideas and graphs. If this foundation is provided in kindergarten, the students will be able to understand more complex graphing ideas in the higher grades.

When I have worked as a substitute in kindergarten classrooms, I have used pictographs. I have found these pictographs to be helpful with this age level. Also, we constantly work with concrete objects in kindergarten classrooms. Some teachers use counters, others use shapes and other use base ten rods or other types of materials.

Often, when I substitute in the first or second grade classrooms, the children complete activities similar to the ladybug activities which we viewed in the video. The children observe data and then on a record sheet use pictures or numerals to record the data. The data used in first grade and second grade classrooms are seeds, plants, roots and flowers. I felt the lady bug activity was a great idea and I enjoyed the video. I am studying ASL presently. And during the past year, I was able to assist and observe in bilingual classrooms so I enjoyed that aspect of the video also.

Also, in second grade classrooms , the concepts of Venn Diagrams are also used to display data. A variety of topics can be represented with Venn diagrams. They are also used in language arts, social studies and math. It is a great way to use literature across the curriculum and integrate mathematics into a reading lesson or social studies lesson.

The intermediate classrooms use bar graphs, circle graphs and tally charts. I have also taught concepts such as mean, median and mode to 4^th grade students. I have not taught the concept of box and whisker plots and it would seem that this concept would be taught in 7^th grade. I do not substitute in the middle schools.

The strategies presented in this workshop were strategies that I have used as a regular classroom teacher and as a substitute. I often use cooperative groups and student presentations. These strategies allow students to become effective communicators of mathematical concepts.

I feel that my experiences and skills with mathematics have prepared me to teach data and statistics at an elementary level. I worked for several years with local governments and I used the census materials frequently. Also, as a graduate student , I took two statistics courses. Therefore, I am familiar with data collection and the presentation of data. The topic of data and statistics is one with which I am comfortable.

 

Activities That I Will Incorporate Into My Lessons

I will develop a second grade activity for graphing from this lesson. I will plan a lesson that will involve students creating a class graph. The children will be asked to identify either objects in the classroom or outside the school in the playground or nature trail. The students will identify living animals or living plants and will record it on a data sheet. The class will then make a graph showing the results.

Another second grade activity that I will design a lesson for is a class survey. The students will take a survey of the types of socks their group members are wearing and record the results on an Activity Sheet. The students will work cooperatively to complete the graph. The students will create a class graph.

What’s The Big Idea? -Elementary Math Recertification Course

Workshop # 1

Patterns and Functions: What Comes Next ?

I particularly enjoyed viewing the Patterns and Songs segment for preschool and kindergarten . The musical activities presented , Hokey Pokey and Old McDonald are excellent tools for introducing patterns and predictability to the students in preschool and kindergarten. I have used snap it cubes to introduce the concept of predictability and patterns. I have also used shapes and colors during Calendar Math activities to introduce the concepts in kindergarten. I currently work as a certified teacher substitute and often work in kindergarten and first grade.
Also, the Guess My Rule Activity can be used by students in K-8 and can be modified for each grade level. I have never used this activity in a classroom. I enjoyed the activity of identifying the mathematical rules from the participating sites and I am sure that students will also enjoy this activity. It encourages problem solving skills and gives the students a break from paper and pencil activities.
Several good points were made regarding the use of small groups during math instruction. I have used cooperative learning as a classroom teacher and as a substitute teacher. I have found that cooperative learning groups can create a noise level which the teacher may not sometimes feel comfortable with. However, the benefits of cooperative learning make this strategy an important part of classroom instruction. The social skills and critical thinking skill associated with cooperative learning are valuable for primary classrooms.
Another effective strategy was provided by the middle school math teacher during the discussion of cooperative learning. He suggested that the teacher may want to allow students to work in pairs for activities. In addition, the teachers may wish to incorporate a time for interaction with each team of partners. I have also used teacher/student conferences as a classroom teacher and as a substitute teacher. I most often use this strategy in language arts and reading. I find that it is a very effective strategy, but involves planning enough time to conference with all students. Also, I plan other activities for students while I am conferencing with one students. However, with this activity the other pairs will be working on their math activity so planning an additional activity will not be necessary. Finally, I think the cooperative learning segment which we viewed demonstrated how to encourage creativity and higher level thinking.
I have used the activity of measuring the volume of a solid figure while teaching a math lesson in a fifth grade classroom. I used the formula l X w X h. I used a shoe box for my my visual aid because I was teaching the volume of a rectangular prism. It was a successful lesson as far as completing the goals and objectives of the lesson . However, I did not have base ten rods or Cuisenaire rods. The information from this workshop will be helpful in future lesson planning. Also, I did not include the surface area in the lesson that I taught , I only introduced the concept of volume . However, I think the strategy of teaching both  volume and surface area  is  an excellent idea. The use of tables, graphs and rules to represent functional relationships was very effective. Cooperative Learning reinforced a variety of skills with the students.
I am a visual learner who also enjoys kinesthetic activities where I can receive hands on stimulation. I prefer to be given visuals with mathematical instructions to coincide with symbolic representations. I felt that this workshop provided materials for the different types of learning styles in a classroom and was comprehensive in the approach to this concept.
Activities that I will Incorporate in My Lessons
I will incorporate many concepts into my lessons. As a substitute teacher, I work with students in K-5. Therefore, I will be able to use many ideas from this workshop. I will develop an emergency substitute plan for K-1 which incorporates geometry , patterns and spatial sense. One lesson that I would like to develop for kindergarten is a lesson with animal patterns. I will also include in the lesson a section where the students use link cubes and form patterns such as red, blue, red, blue, or red, blue, red, red, blue. I would also like to use a lesson with a spider web pattern. Children would spin their own webs using string and paste and would make patterns using circles, line and repetition.
For the intermediate students, I would like to use the ideas of patterns and relationships in a lesson on measurements. I already have a substitute lesson for volume. It is based on the volume of a rectangular prism. It is for fifth grade students. However, I would like to add to this lesson an activity with surface area. The students will make observations and comparisons based on their measurements.  They  will also design a graph based on their observations.

Multiplication Squares-Math Lesson Plan

Final Course Project

Mathematics: What's The Big Idea ?

Grades K-8

Gabriella Robinson

July 23, 2011

The handouts for this lesson are posted on classwiki45.wikispaces.com   on the
professional development page.

Bunches and Bunches of Bunnies

Multiplication Squares

4^th Grade

Multiplication, Square Numbers
Lesson Overview


This lesson is for fourth grade students. The students will learn basic multiplication facts and will demonstrate an understanding of multiplication. The teacher will use the story Bunches and Bunches of
Bunnies to introduce the concept of square numbers. The students will listen to Bunches and Bunches of Bunnies as a shared reading activity. The teacher will then introduce two math activities to reinforce the concept of multiplication squares.
Summary : The students will create multiplication squares to help them understand the concept of square numbers. This activity will help students to understand multiplication's relationship to repeated addition.
SC Curriculum Standards-Math
4-2 Number and Operations
4-2.3 Apply an algorithm to multiply whole numbers fluently.

• Multiplication facts to 12 (D.1)
• Choose the multiples of a given number up to 12(D.2)
• Choose numbers with a particular product (D.11)

4-3 Algebra

4-3.4 Translate among letters, symbols, and words to represent quantities in simple mathematical expressions or equations.

• Write variable equations to represent word problems (G.5 )

Materials
Bunches and Bunches of Bunnies by Louise Matthews
Grid Paper
Scissors
Paste
Crayons
Construction Paper
Square Facts Worksheet
Counters
Activity Sheet 16
Cards
Calculators




Background for Teachers
A squared number is a number that is a result of multiplying an integer by itself. Any squared number can be represented in a square array. You can write each squared number as a product using an exponent.
4² =16
Intended Learning Outcomes

1. Demonstrate a positive learning attitude toward mathematics.
2. Become mathematical problem solvers.
3. Reason mathematically.
4. Communicate mathematically.
5. Make mathematical connections.
6. Represent mathematic situations.

Web Site

Aunty Math (Grades K-5)

Synopsis: A visit to relatives can be a great time to learn math. Aunty Math, has great math challenges for students in K-5. The students will learn the use of multiple intelligences in problem solving. Students submit their solutions to the challenges, and teachers can explore the mathematics behind the challenges.

www.dupagechildrensmuseum.org/aunty

Strategies
Manipulatives- counters, multiplication squares
Modeling
Shared reading
Calculators

Instructional Procedures: Invitation to Learn


Shared Reading


Read the book: Bunches and Bunches of Bunnies by Louise Matthews.
Say, "Which is easier to count the bunnies in large groups, or the bunnies by twos, threes and fours? Discuss their reasoning. Ask students to predict mutiplication sentences for the different groups. Next discuss the squares of numbers. Give children counters. Reread the story, write each multiplication sentence on chart paper and ask children to model it with their counters.


Multiplication Squares


Give pairs of children, Grid Paper. Also provide the students with scissors, paste, crayons and construction paper. Ask children to color and cut out a model for each multiplication sentence( this is the chart paper that was used during the Shared Reading activity, above ). Have children paste these models on construction paper and then write a corresponding multiplication sentence beneath it. The students should be able to describe the shape of each model ( each model forms a square). Examples of the models and multiplication sentences are provided in the handouts section of the lesson plan.






Modeling Multiplication Facts


Provide students with Activity Sheet 16 to make a booklet. The students will also need scissors and paper. Each pair should be assigned a multiplication table, such as the four table. Students will write a multiplication sentence on each page of the booklet, and cut and paste carrot bunches to illustrate the sentence. The students will staple the booklets together and share them with the class. ( An example, of the booklet is included in the handouts section).


Extending the Lesson


Discuss the squares of numbers. Ask the students to fold a sheet of paper. Ask them to half the paper again. Can you fold it into half eight more times? Show the math involved.


Additional Extensions


Students can color in the square numbers on a multiplication chart. Look for patterns in the chart. ( the square numbers will form a diagonal on the chart).


Predictions
Ask the students to predict if the product of any number multiplied by itself will form a square. Ask children to choose a number between 12 and 20 and multiply the number by itself. Then make a model of it on grid paper. Discuss why these numbers are called square numbers.


Calculator
Exploring Area with the TI -10
Activity – The teacher will provide each student with 49 cards.
Ask the students " How many cards cover the desktop?"
"How might your cards be arranged to count with your TI -10 (rows and columns)?"
The following instructions are given for TI-10 calculators. However, your students may use other calculators with this activity.


Press the on button.
Press AC to clear anything previously stored.
Press clear. The screen is blank and the memory is clear.


Press Opl to begin counting.
Press + 7 because you will be counting cards by rows of seven.
Press Opl to let the TI -10 know that you are ready to count.
Press 0 to begin counting at 0.
Press Opl to continue counting.
When you have counted seven rows the TI -10 displays
42 +7
7 49


Answer: Area is 7X7=49 or 7² =49




Pass out two centimeter grid paper.


Question to ask:


What might you say about the size of the squares on the grid paper?
(Answers should suggest they are all the same size)


How might you and your partner find the number of squares to cover the desktop with grid paper?


How might the TI-10 help?


( The two centimeter grid paper and an example for this activity is included in the Handouts section of the lesson plan. In the example in the handout sections I used seven rows and seven columns. However, the number of rows in columns will vary depending on the size of the desks in your classroom.)


Homework and Family Connections
After completing several activities in class, ask the students to complete the Square Facts sheet at home. Ask the students to have a family member complete the game with them. The family member can sign the activity sheet to indicate that they have worked together to enhance their mathematical understanding.
( The Square Facts sheet is included in the Handouts section of the lesson plan)


Encourage students to play any of the mathematics related board games at home to reinforce their math skills: Dominoes, Connect 4, Rummikub, Triple Yahtzee, Yahtzee, Backgammon, Chinese Checkers, Tower of Brahams, UNO.


Assessment Plan:



Journal Activity : Have students explain what square numbers are. Use pictures, words and numbers to explain what 5² is.




Differentiated Instruction


For Auditory and Kinesthetic Learners: Use a multiplication rap such as Hap Palmers' Multiplication Rap to reinforce multiplication facts. Students can listen to these raps at a learning center and learn the facts.


For Visual Learners: Students can complete math activities at file:///C:/Documents%20and%20Settings/Gabriella%20Robinson/My%20Documents/www.funbrain.com or mathworld/wolfram.com in the classroom computer center.