Virtual Manipulative - Money Grades 3-5

This manipulative is very useful for students who may need extra practice with basic money concepts. There are three skills that students can practice involving money. Students can work with making coins equal to $1.00, identify how much money is shown, and placing the requested amount into the box. This is a very basic manipulative but would be great for lower level kids or kids who need some reinforcement.

Cuisenaire Rods Lesson Plan - Plots and Paths

Anticipatory Set:
Complete/Review Do Now and homework

Learning Expectations:
* compute the perimeter and area of shapes
* compare shapes with the same area
* discover that shapes with the same area can have different perimeters

Activities:
* Arrange three Cuisenaire Rods—two reds and a yellow—on grid paper so that the rods lie within the grid lines and at least one centimeter of each rod touches another. Trace around your shape.
* Remove the rods and show the class your “plot.” Have children confirm that the area of your plot—the part that could be covered with grass—is 9 square units.
* Ask children to figure out how long a “path” is needed to go completely around the edge of your plot.
* Reinforce the understanding that the perimeter of your plot—the “path”—is 16 units by counting and numbering each unit.
* What happens when you make different-shaped plots with the same set of Cuisenaire Rods? Use 2 whites, 2 reds, 2 light greens to create a plot. Record on the grid paper and calculate the perimeter and the area. Use the same 6 rods to create additional plots. Record and calculate perimeters and areas. Discussion Questions: What is the shortest possible perimeter? What is the longest? How are plots with the same-length paths the same? How are they different?
* FasttMath, Virtual Manipulatives

Assessments:
* teacher observations, student-directed discussion, drawings

Materials:
* communicators, cuisenaire rods, cm grid paper

Tech Infusion:
Promethean board - flipchart, laptops, voters

Accomodations/Modifications:
* teacher designed groups
* differentiated assignments/activities (centers to reach all levels)
* extended time-classwork/assessments(when needed)
* restructured homework assignments for both above level and below level students
* use of manipulatives/graphic organizers
* extension activities/alternative assignments
* organizational strategies - notebooks/book boxes/folder systems
* cloze-notes/study sheets/practice sheets for further reinforcement
* modified assessments - M/C, SCR, ECR, O-E
* preferential seating
* seating near positive role model
* encouraging independence/student initiative
* includes a rich variety of resources, media ideas, methods and tasks
* proximity to teacher
* personalized monitoring tools (checklists, goal sheets, thumbs up/down level understanding monitors)
• Homework: Math - extended-constructed response
• Standards: MA.4.4.2.4 D.2.b, MA.4.4.2.4 E.1, MA.4.4.2.4 E.2

Virtual Manipulatives - Week 10 - Triominoes

This manipulative is found in Geometry - Grades 3-5. In triominoes students manipulate pieces to create a pattern. Pieces can be turned and flipped and need to be matched according to the color. When pieces are matched correctly they stick together. This is beneficial to help students practice manipulating pieces and visual thinking skills.

Buidling to Spec - Cuisenaire Rod lesson plan #2

Lesson Plan – J. Pisano
Building to Spec – Cuisenaire Rods Grades 3-4
Complete/Review Do Now and homework

Learning Expectations:
*construct shapes that satisfy a given set of conditions
* give and follow a set of directions
* compare different shapes that may result from the same set of clues

Activities:
* Give a set of clues and have students build a Cuisenaire Rod shape that fits the clues – allow pairs of students to adjust and discuss their solutions after each clue is given.
• The shape is a hollow square
• The shapes uses more than one color
• The shape has exactly six rods
• One of the rods is purple
* Share solutions and discuss how they are alike and different. Students complete On Their Own
* How many Cuisenaire Rod shapes can you build that satisfy a given set of clues?
1. Work with a group. Pick a set of clues. You will take turns removing clues from the envelope and reading them aloud.
2. After the first clue is read, you should make a shape that satisfies the clue. Check one another’s work. Your shapes may or may not look alike.
3. After the second clue is read, you may make changes to your shape to satisfy both clues. Check one another’s work.
4. Read the other clues, making any necessary changes.
5. Compare the final shapes to make sure that they each satisfy all 4 clues. Record your shapes.
6. When your group is finished return clues to envelope and choose another to repeat the activity.

Discussion questions – In what ways did you change your shape to satisfy a new clue? What type of clues did you find the hardest to satisfy? Explain. Do you think the order in which the clues came out of the envelope made a difference? Would a different order have made it easier to build the shape? Explain.

Extending the Activity
1. Students create a shape using 6 rods or fewer and write as many clues as they can to describe the shape.
2. Students work in pairs to create a shape and write a set of 4 clues that describes the shape. Exchange sets of clues and try to solve.

Assessments: teacher observations, game play and follow up discussion

Materials: Cuisenaire rods, 1-cm grid paper, clues
Tech Infusion: Promethean board – flipchart, laptops – Virtual Manipulatives website

Accomodations/Modifications:
* teacher designed groups
* differentiated assignments/activities (centers to reach all levels)
* extended time-classwork/assessments(when needed)
* restructured homework assignments for both above level and below level students
* use of manipulatives/graphic organizers
* extension activities/alternative assignments
* encouraging independence/student initiative
* includes a rich variety of resources, media ideas, methods and tasks
* proximity to teacher
* personalized monitoring tools (checklists, goal sheets, thumbs up/down level understanding monitors)

Homework: short-constructed response review
Standards: MA.4.4.5 A.1, MA.4.4.5 A.2.b, MA.4.4.5 A.5, MA.4.4.5 B.1.b, MA.4.4.5 B.2, MA.4.4.5 B.3, MA.4.4.5 D.2, MA.4.4.5 D.3, MA.4.4.5 D.4, MA.4.4.5 F.1

Geoboards Lesson - Area of Four

This lesson is found under Grades 3-4 Geoboards - Area of Four - Children use geoboards to make different shapes, each with an area of 4 square units.

Anticipatory Set:Complete/Review Do Now and homework

Learning Expectations:
· make shapes with a given area
· use a variety of methods for finding area
· discover that different shapes can have the same area

Activities:
Can you make different-looking Geoboard shapes that have the same area?
• With a partner, make at least 9 different Geoboard shapes, each with an area of 4 square units. Work together to decide how to measure the area of each shape.
• Record your shapes on geodot paper.
• Now choose 2 of your shapes to record on large geodot paper.

Have children take turns posting their larger drawings. Ask children to compare the posted shapes to see if any are congruent. Have them remove any duplicate shapes so that the posted solutions are all different.
Use prompts such as these to promote class discussion:
v How did you find new shapes?
v How did you make sure each shape had an area of 4 square units?
v For which shapes was finding area easy? For which shapes was it harder? Explain why.
v What do you notice when you look at the posted shapes?

Extending the Activity
1. Have children create categories by which to sort their posted shapes. Some examples might be number of sides, square corners/no square corners, parallel sides/no parallel sides.
2. Have children repeat the activity for shapes with areas of 3 or 5 square units.

Assessments:teacher observations, shapes, student-centered discussion

Materials/Tech Infusion:communicators, geoboards, laptops, Promethean board, Virtual Manipulative – geoboards

Accomodations/Modifications:* teacher designed groups* differentiated assignments/activities (centers to reach all levels) * extended time-classwork/assessments(when needed)* restructured homework assignments for both above level and below level students* use of manipulatives/graphic organizers* extension activities/alternative assignments* modified assessments - M/C, SCR, ECR, O-E* encouraging independence/student initiative* includes a rich variety of resources, media ideas, methods and tasks

· Homework: Math – open ended response question

Geoboard Lesson Plan - 3, 4, 5 and more

This lesson comes from Geoboards - Grades 3-4 on the lesson plan disk. This lesson allows children to make polygons with different numbers of sides on their Geoboards. They then investigate the similarities and differences.

Anticipatory Set:Complete/Review Do Now and homework
Learning Expectations:
*classify polygons according to the number of sides
* discuss attributes of geometric shapes
* use the language of geometry
Activities:
* How many different polygons can you make on the Geoboard?
• Work with your group. Each of you make a closed shape—a polygon—with 1 rubber band. Each person’s shape should have a different number of sides.
• Compare your shapes. Once you agree that each shape has a different number of sides, record your shape on geodot paper.
• Repeat this process until your group thinks it has made shapes with every different number of sides that it can.
• Record your square. Think about how you could rearrange the tiles to form a different solution. Look for other solutions. If you find any, record them, too. Be ready to explain the decisions you made.
** Students work with both geoboards and the virtual manipulatives.

Thinking and Sharing
Post children’s shapes into columns by number of sides. Begin by calling for shapes with three sides and continue by calling for shapes with an increasing number of sides. Label each column by the number of sides. Then, when all the shapes have been posted, write the appropriate geometric names above each column—Triangles, Quadrilaterals, Pentagons, Hexagons, Heptagons, Octagons, Nonogons, Decagons, and so on.

Use prompts such as these to promote class discussion:
* Look at the shapes in one column. How are they alike? Are any exactly the same?
* How are the shapes within a column different? Why are different-looking shapes in the same column?
* Which shapes were the hardest to make? the easiest?
* Do you think it is possible to make shapes with even more sides on the Geoboard? Explain.

Assessments:teacher observations, shapes, student-centered discussion

Materials/Tech Infusion:communicators, geoboards, laptops, Promethean board, Virtual Manipulative – geoboards

Accomodations/Modifications:
* teacher designed groups* differentiated assignments/activities (centers to reach all levels) * extended time-classwork/assessments(when needed)* restructured homework assignments for both above level and below level students* use of manipulatives/graphic organizers* extension activities/alternative assignments* modified assessments - M/C, SCR, ECR, O-E* encouraging independence/student initiative* includes a rich variety of resources, media ideas, methods and tasks
**** Homework: Math – open ended response question

Virtual Manipulatives - Geoboard Coordinate

I like this manipulative found under Geometry grades 3-5. This is similar to the basic geoboard manipulative where the students can place rubber bands and make shapes. It also shows the perimter and the area of each shape. This coordinate manipulative is useful to introduce students to the 4 quadrants and negative numbers. I have been working with my students on graphing ordered pairs and this allowed them to continue to explore the negative numbers and get comfortable working with them while creating their own designs.

Lesson Plan - Shopping for Rods

Cuisinaire Rods - Grades 3-4 Shopping for Rods Activity

Anticipatory Set: Review homework and complete Do Now

Expectations: ~compute mentally~ work with money concepts~ use ratio and proportion~ discover relationships among Cuisenaire Rods

Procedure: Revisit the procedure for determining the value of the pattern blocks based on their fractional parts of the whole hexagon to set the stage for this activity.Tell students to imagine that the Cuisenaire Rods are for sale and that the white rod costs $1.00. Invite volunteers to explain why the red rod should cost $2.00. Once it is established that the red should cost twice as much as the white because it is twice as long, have children figure out the cost of a rod of each of the other colors. Show children that the cost of some rods can be determined in more than one way. Point out that the cost of the brown rod, $8.00, can be found by counting by ones, by twos, or by fours.
How many Cuisenaire Rods could you “buy” with $10.00?
• Work with a group. Pretend that your group has $10.00. You must spend it all to “buy” Cuisenaire Rods.
• To find the price of a particular rod, one of you spins a spinner.
• Use the results of the spin to find the prices of other rods. For example, if you spin “1 white rod costs $2.00,” a light green rod will cost $6.00 because it is 3 times longer than the white rod.
• Use the prices of the rods for your spin to answer these questions: What is the least number of rods you could buy for $10.00? What is the greatest number of rods you could buy for $10.00? What number of rods between the least and greatest numbers could you buy for $10.00?
• Take turns spinning until each member of the group has had a turn with a different starting price. For each turn, find the price of the rods and answer the questions above.
• Record your answers and any patterns you notice.

Writing and DrawingAsk children to pretend that they work for the company that makes Cuisenaire Rods. Have them design an advertisement that includes a price list for the rods based on the fact that one yellow rod costs $0.75.

Extending the Activity Have children create a picture or a design with Cuisenaire Rods and then spin the spinner to figure out the “cost” of their picture/design.

Lesson Plan - Color Tiles

Jennifer Pisano - Lesson Plans for Mon, 3/29/2010

Anticipatory Set:Complete/Review Do Now and homework
Learning Expectations: -use logical reasoning-develop a design that satisfies specific conditions-discover a new solution based on an old one

Activities:* Can you follow a set of rules to form a square arrangement of Color Tiles?
Work with a partner. Use 16 Color Tiles to form a square according to these rules:
* The square must have 4 of each color of tile.* No 2 tiles of the same color may touch along a side.* No 2 tiles of the same color may touch at a corner.* The order of the colors in each row must differ from the order in every other row.

• Record your square. Think about how you could rearrange the tiles to form a different solution. Look for other solutions. If you find any, record them, too. Be ready to explain the decisions you made.
** What strategies did you use to arrange your tiles?
Did you ever get “stuck”? If so, how did you get “unstuck”?
How could you be sure that your design followed all three rules?
Do you see any patterns in your design? Describe them.
Which other squares are exactly like yours? Which are different? How are they different?

Assessments:teacher observations, squares, student-centered discussion

Materials:communicators, color tilesTech Infusion:Promethean board - flipchart

Accomodations/Modifications:* teacher designed groups* differentiated assignments/activities (centers to reach all levels) * extended time-classwork/assessments(when needed)* restructured homework assignments for both above level and below level students* use of manipulatives/graphic organizers* extension activities/alternative assignments* modified assessments - M/C, SCR, ECR, O-E* encouraging independence/student initiative* includes a rich variety of resources, media ideas, methods and tasks

· Homework: Math – open ended response question
· Standards: MA.4.4.2.4 A.2.c, MA.4.4.2.4 A.5, MA.4.4.5 C.1

Virtual Manipulatives #8 - Mastermind

This manipulative is found in grades 3-5 Numbers and Operations. This is a game similar to the color tile logic game where the object is to guess the order of colored pegs. You win the game by discovering the colors of the four peg solution. You have 8 chances to correctly guess answer. After each guess you receive feedback consisting of black and white pegs. The number of black pegs is the number of correct pegs in your guess. That is, for example, one black peg tells you that exactly one of the pegs in your guess is the right color in the right place, but you don't know which one is correct. The number of white pegs is the number of pegs in your guess that are the correct colors but that are not placed in the correct positions, so two white pegs would tell you that two of your four pegs are correctly colored but not in the right locations.
This is a challenging game that students at all different levels can play since you can switch the number of colors used from 2 colors to 6 colors.

Lesson Plan - Square Numbers - Grades 3-4

Jennifer Pisano - Lesson Plans for Color Tiles and Pattern Blocks
Math
Anticipatory Set:
Complete/Review Do Now and homework

Learning Expectations:
* learn the characteristics of square and triangular numbers
* recognize patterns *make predictions based on patterns

Activities:
*show a square with one Pattern Block - use orange blocks or color tiles to make the next bigger square. Set up a table and have record what they have done. Now show the green triangle and model how to build the next bigger triangle with green blocks. Point out that in building bigger triangles, one new row is added to a side of the previous triangle, leaving spaces between blocks.
~What patterns can you find in the numbers of Pattern Blocks that can be used to make squares and triangles?• Using the orange blocks, work with your partner to build increasingly larger squares.• Record, each time, both the number of blocks you added to build the next bigger square, and the total number of blocks in the new square.• Record the numbers through the eighth square, but build squares only until you discover the pattern that will give you all the numbers you need.• Now use the green blocks to build increasingly bigger triangles. Build new triangles by adding blocks to one side of the previous triangle. All blocks should be positioned the same way, and there should be spaces between all the blocks• Record, each time, through the eighth triangle, but build only until you discover the pattern.• Be ready to discuss the patterns your tables reveal.

Assessments:
* teacher observations, student-centered discussion, patterns

Materials:
* pattern blocks, grid paper, color tiles

Tech Infusion:
Promethean board - flipchart, laptops, activotes for follow-up

Accomodations/Modifications:
* teacher designed groups
* differentiated assignments/activities (centers to reach all levels)
* use of manipulatives/graphic organizers
* extension activities/alternative assignments
* seating near positive role model
* encouraging independence/student initiative

• Homework: Math - write about the patterns that were discovered in the blocks
• Standards: MA.4.4.2.4 A.5, MA.4.4.3.4 A.1.a, MA.4.4.3.4 A.1.c



Sample Table for square - make a similar table for triangle numbers

Figure # 1 2 3 4 5 6 7 8
# blocks 1 4 9 16
# you added 0 3 5 7

Virtual Manipulative # 7 - Fractions - Parts of a Whole

This manipulative is found in grades 3-5 Numbers and Operations and is a great way to introduce fractions as parts of a whole. It allows students to select the number of pieces/denominator and then shade pieces and see the fraction. This is good for students with little or no fraction experience and also as a review for other students who are beginning a fractions unit.

Virtual Manipulatives #6 - Fractions - Naming

This manipulative found in Grades 3-5 Numbers and Operations is good for students who are just learning to name fractions as parts of a whole. It allows studnets to see different shapes split into equal groups and name the numerators and denominators. I would use this for my students who have little or no background experience with naming fractions as an introduction and also with my other students as a review.

Pentominoes

Here is another interactive experience to share with your students. This activity is listed under grades 3-4 but I am sure that middle school students would enjoy it as well!

Problem Solving with Pentominoes

Function Machine

Here is the link for the function machine game grades that I showed in class last Monday.

Grades 3-4

Grades 5-6

Enjoy!

Virtual Manipulatives 5 - Spinner

The manipulative I chose to work with was the Spinner - found in Grades 3-5 Data Analysis and Probability. I chose this particular manipulative to use in one of my math centers related to graphing and probability. Students are able to work with spinners that have different colored sections. This is a perfect resource for differentiation as the students who are having difficulty with probability can work with smaller spinners/fewer colors, while the students who need enrichment or extension activities can use spinners with more colors and sections.

Color Tiles Lesson Plan 2 - Be a Logician!

Lesson Plan – J. Pisano
Be a Logician! Color Tiles Grades 3-4

Anticipatory Set: How could you guess the order of objects if you couldn't see them?

Learning Expectations:
*formulate hypotheses in order to satisfy conditions
*develop deductive reasoning skills

Activities:
* Be a logician! Use color tiles to play a game in which students apply logical thinking in order to guess the sequence of colors of hidden tiles. Make a row of three Color Tiles in this order, from left to right, and keep it hidden. Tell children that you have hidden a row of three tiles, each of a different color. Challenge children to guess the colors of the tiles and their order—first, second, and third. Explain that after each guess you will write a clue on the chalkboard. For each color guessed correctly, you will draw a circle. For each position guessed correctly, you will draw a dot inside the circle. Call for one volunteer’s guess, record it on the flipchart. Draw the appropriate clues, “What do we know from this?" Keep on calling for guesses and recording clues until the correct color and order of the tiles have been guessed.
* Play Be a Logician! Here are the rules.
1. This is a game for 4 or more players. The object is to guess the colors of 3 Color Tiles and their order, from left to right.
2. Players decide who will be the 2 Leaders and who will be the 2 Logicians.
3. The Leaders build a row of 3 Color Tiles, each tile a different color. They keep the tiles hidden from the Logicians. (rotate groups to use the laptops to play the game) NLVM – Color Tiles
4. The Logicians make guesses by naming 3 colors of tiles in order.
5. After each guess, the Leaders give a clue about how close the guess was. The clue must have 2 parts:
~ It must tell how many colors in the guess are correct.
~ It must tell how many color tiles in the guess are in the correct position.
For example, suppose the secret row of tiles was blue-green-yellow and the Logicians guessed red-green-blue. The Leaders would give this clue: “Two of the colors are correct, and 1 tile is in the correct position.”
6. The Logicians record each guess and clue.
7. The game ends when Logicians guess the correct colors and order.

• Play several games of Be a Logician! Make sure that everyone in the group has a chance to be a Leader and a Logician.
• Be ready to talk about good guesses and bad guesses.

Discussion questions - What was the hardest part of playing this game? What was the easiest? Which clue(s) helped you to decide which three colors were used? Which clue(s) helped you to decide the positions for the three colors?

Extending the Activity
1. Ask children to list all possible solutions (permutations of four colors) in a game of Be a Logician! in which the four colors of tiles are used in four positions.
2. Have children play Be a Logician! again, this time with three Color Tiles, two of one color and one of another color.

Assessments: teacher observations, game play and follow up discussion

Materials: communicators, color tiles, laptops\
Tech Infusion: Promethean board – flipchart, laptops – Virtual Manipulatives website – Color Tiles gr. 3-5

Accomodations/Modifications:
* teacher designed groups
* differentiated assignments/activities (centers to reach all levels)
* extended time-classwork/assessments(when needed)
* restructured homework assignments for both above level and below level students
* use of manipulatives/graphic organizers
* extension activities/alternative assignments
* encouraging independence/student initiative
* includes a rich variety of resources, media ideas, methods and tasks
* proximity to teacher
* personalized monitoring tools (checklists, goal sheets, thumbs up/down level understanding monitors)

Homework: short-constructed response review
Standards: MA.4.4.5 A.1, MA.4.4.5 A.2.b, MA.4.4.5 A.5, MA.4.4.5 B.1.b, MA.4.4.5 B.2, MA.4.4.5 B.3, MA.4.4.5 D.2, MA.4.4.5 D.3, MA.4.4.5 D.4, MA.4.4.5 F.1

Private Universe - Workshop 4 - Thinking like a Mathematician

The main thing I took from this video was the importance of engaging your students in the lessons, especially in mathematics. It is easy to present information to a group of students from a textbook and in a lecture format. With this approach a majority of the students will "check out" and that is when behavioral problems will occur. In classrooms where math instruction has changed to hands-on, inquiry based instuction, students are taught that there is more to solving problems than simply getting the right answerand the students are more engaged. This approach of inquiry also allows the less confident students to realize they may more know than they originally thought they did. If this type of instruction begins early in the grade levels students would develop more confidence in their mathematical abilities. Teaching that moves from the traditional - teacher has the answers and tells the students who is right and/or wrong to an inquiry-based learning environment the students develop more confidence in their abilities to learn.

Private Universe - Workshop 3 Inventing Notations

As I watched this video all I could think about was how important it is to allow students to express themselves in their own ways. When we allow the students to explore and in turn explain their thinking they learn so much more than simply feeding them the process and the right answers. When we give them the time to develop their own processes and proof we are allowing them to become problem solvers and thinkers and these skills will only benefit them in the future. This video sparked my interest and I wonder how my fourth grade students would go about solving this pizza problem and how they would display and prove their answers. I can't help but wonder will they make any connections to the tower problem that they were presented with weeks ago. I will be presenting this problem to my students and will bring the results to class to share.

Virtual Manipulatives 4 - Function Machine

The virtual manipulative I will work with this week is Function Machine - Grades 6-8 Numbers and Operations. I was looking for something that my afterschool tutoring groups could use as a reinforcement activity for input/output tables. This was a weakness of the group based on an assessment done at the beginning of the tutoring program. This manipulative seems to be pretty good. It gives the students an opportunity to see a function machine and see the table that is created. When they put in the numbers 1, 2, 3 and 4 the computer tells them the output numbers. They have to use what they know to determine the pattern and fill in the remainder of the table, numbers 5 - 7. Once they figure out the pattern they can move on to a new function. I will use this with my group and see how they do with it. It does not seem to be as exciting and attention grabbing as some of the other virtual manipulatives we have explored.

Lesson Plan - Color Tiles

In this lesson students will use the color tiles to continue their exploration of perimeter and area. This lesson will be used with my after school tutoring group of fourth graders. The group was designed to give the students who either did not pass or just barely passed the NJ ASK 3. I gave a LEARNIA assessment test at the beginning of the tutoring sessions and found that perimeter and area were weaknesses for the group. This activity will help to reinforce these concepts.

Lesson Plan - Color Tiles
This lesson is based on: "Changing Areas" Grades 3-4

Anticipatory Set:
Complete/Review Do Now and homework

Learning Expectations:
* measure to find the perimeter of a shape
*develop the understanding that figures with the same perimeter can have different areas

Activities:
* Display this shape made from Color Tiles of one color. Have students copy it. Show students how to move the edge of another Color Tile around the shape to measure its perimeter. Have a volunteer give the perimeter. Confirm that the perimeter may be expressed as 10 units or 10 inches. Have another volunteer give the area. Confirm that the area may be expressed as 4 square units or 4 square inches. Ask students to use four more Color Tiles to make a different shape in which each tile touches at least one other tile along a complete side. Have students find the perimeter and the area of their shape and share the results.
~~How many different Color Tile shapes can you make that have the same perimeter?
• Work with a partner. Use 3 to 8 Color Tiles to make a shape. Each tile in the shape must touch at least 1 other tile along a complete side.
• Record your shape.
• Find the perimeter of your shape and write it above the recording.
• Now use Color Tiles to make as many different shapes as you can that have the same perimeter. Record each shape and its area.
Thinking and Sharing
After you made your first shape, how did you go about making different shapes with the same perimeter?
Do you see any patterns among your shapes? Explain.
Do you notice a relationship between shapes with the same perimeter and the areas of those shapes? Explain.

Assessments:
* teacher observations, student-centered discussion, color tile shapes

Materials:
* color tiles, color tile grid paper

Tech Infusion:
Promethean board - flipchart, laptops

Accomodations/Modifications:
* teacher designed groups
* differentiated assignments/activities (centers to reach all levels)
* extended time-classwork/assessments(when needed)
* restructured homework assignments for both above level and below level students
* use of manipulatives/graphic organizers
* extension activities/alternative assignments
* organizational strategies - notebooks/book boxes/folder systems
* cloze-notes/study sheets/practice sheets for further reinforcement
* modified assessments - M/C, SCR, ECR, O-E
* preferential seating
* seating near positive role model
* encouraging independence/student initiative
* includes a rich variety of resources, media ideas, methods and tasks
* proximity to teacher
* personalized monitoring tools (checklists, goal sheets, thumbs up/down level understanding monitors)


Homework: Tell students to imagine that a zoo needs help designing a play area for monkeys. Students can help by making a design with a perimeter of 36 units (or yards) of fencing. Direct students to use Color Tiles to make their designs. Then have them record the design that gives the monkeys the most room to play. Students can write a note to the zoo telling why their design would make a good play area for monkeys.

Enrichment: Challenge students to build two Color Tile shapes, one with a perimeter of 20 units (or inches) and having the least possible area and the other with the same perimeter and having the greatest possible area.

Virtual Manipulatives 2 - Peg Puzzle and Towers of Henoi

After the experience of trying to solve these puzzles in class and feeling frustrated I was a little concerned about sharing these with my fourth graders. Since we had just received our laptops in our classroom and we had a little extra time after a lesson I decided to show them both puzzles on the interactive board. I was surprised at the fact that some of them had already seen the peg puzzle: "I play this at Cracker Barrel!" was the response of one of the boys in my class. They were very excited to be given the opportunity to try both puzzles. I left a group by the interactive board and the rest of the students went onto the laptops. They spent about 15 minutes totally engaged. They were excited and some were experiences frustration. When I spoke to those frustrated students and told them how I had difficulty in my class solving them it seemed to ease their frustration and they got back to it. It was interesting to see which students could solve the puzzles and which ones had the difficulty. The next day I had a few students come in and tell me how they showed their parents the puzzles and how they could solve them when their parents had a hard time. This was the confidence boost some of them needed. This is definitely a site that we will continue to use throughout the year in my class.

Lesson Plan - Pattern Blocks

The lesson I chose was dealing with the pattern blocks and would be done a the day after all students completed their free explorations. We discussed the relationship of the pieces to the hexagon. Students were able to quickly see the relationship and this also served as a review of writing fractions. Once we agreed that only the parallelogram, trapezoid, and triangles could be turned into the hexagon I then took it one step further. The lesson involved assigning a value to the hexagon and then based on that value determining the value of the remaining pieces. For example: the hexagon is worth $3.00 what would the value of the remaining pieces be? Once the values were determined we created a design that had a total value of $10.00. We utilized the interactive whiteboard and the virtual manipulatives to model the process. Students were then allowed 10 minutes to create their own $10.00 design. We then discussed how to prove that our designs were actually worth $10.00. Independent practice was to create a $12.00 design and homework was to create a $15.00 design. Students could use either the hands-on pieces or the virtual manipulatives to complete both practice and homework. Lesson plans will be distributed during class.

Lesson Plan
This lesson is based on the lesson: "What's My Shape Worth?"
Anticipatory Set:
Complete/Review Do Now and homework

Learning Expectations:
* investigate relationships among the areas of different shapes
* perform computations with money
* discover that shapes with the same area may look different

Activities:
* Review the characteristics of the pattern block shapes to be used - hexagon, parallelogram, trapezoid, triangle
* Determine the value of the shapes if the value of the hexagon is given - If the value of the hexagon is $0.30 what is the value of the remaining shapes?
* Give students an opportunity to create a design that is worth $1.00. Call for volunteers to put design on Promethean Board (Virtual Manipulatives - Grades 3-5 Geometry Pattern Blocks)
* Discuss ways students went about deciding which shapes to use in their designs.
* Break into centers to create a $12.00 design. (Values are given in directions)
~ Laptops - use Virtual Manipulatives - Grades 3-5 Geometry Pattern Blocks
~ Hands-on - use pattern block pieces - use triangle paper to recreate design
^ work with students who are having trouble with monetary values and building designs

** Enrichment Activity - assign a money value to each of the shapes and create a design that is worth more than $7.00 and less than $20.00.

Assessments:
* teacher observations, designs, student-centered discussion

Materials:
* pattern blocks, trangle paper, colored pencils, communicators

Tech Infusion:
Promethean board - flipchart, Virtual Manipulatives website, laptops

Accomodations/Modifications:
* teacher designed groups
* differentiated assignments/activities (centers to reach all levels)
* extended time-classwork/assessments(when needed)
* restructured homework assignments for both above level and below level students
* use of manipulatives/graphic organizers
* extension activities/alternative assignments
* organizational strategies - notebooks/book boxes/folder systems
* cloze-notes/study sheets/practice sheets for further reinforcement
* modified assessments - M/C, SCR, ECR, O-E
* preferential seating
* seating near positive role model
* encouraging independence/student initiative
* includes a rich variety of resources, media ideas, methods and tasks
* proximity to teacher
* personalized monitoring tools (checklists, goal sheets, thumbs up/down level understanding monitors)

Homework: Math - $15.00 design with pattern blocks - use the shapes to create your design or you may use the Virtual Manipulatives and print out your design

Standards: MA.4.4.1.4 B.4.a, MA.4.4.1.4 B.5, MA.4.4.1.4 B.6.a, MA.4.4.2.4 E.1, MA.4.4.5 C.1

Virtual Manipulatives - 3

As a preview to the lesson on pattern blocks I gave my students the opportunity to freely explore the blocks. The only direction they were given was that their designs must be complete in 2 minutes. Most of the students created symmetrical designs and used all of the shapes they were given. When the designs were completed I took a picture of each of the designs. The next period the students were given a laptop and were instructed to use the pattern block manipulative online and recreate their designs. This allowed the students the opportunity to explore the virtual manipulative and most were successful in this task. A few students were unable to recreate their design exactly, either because it was too large or they were unable to manipulate the shapes on the computer how they had done with the hands-on pieces. Designs were printed and mounted on construction paper as a Math and Technology display. I will bring a few to class to show the finished products.

Lesson Plan - Volume

Currently I am working on geometry with my 4th graders. We used the geoboards to discover what perimeter and area mean and how to calculate both. As a next step we will be exploring volume of rectangular prisms. I looking at the lesson plans on the disk I found a lesson involving base 10 blocks and calculating volume. I would typically introduce volume using connecting cubes but this year I will use the base 10 longs as an introductory lesson and then continue with prisms of different lenths.

Lesson Plan

This lesson is based on: "Building Boxes"

Anticipatory Set:
Complete/Review Do Now and homework

Learning Expectations:
* explore volume of rectangular prisms * utilize spatial reasoning to create prisms
* discover that rectangular prisms with different dimensions can have the same volume
* Develop proficiency with basic multiplication and division number facts using a variety of fact strategies

Activities:
* Review the properties of a rectangular prism- what makes it a prism?
How many different boxes can you make from the same number of Base 10 longs?
*Work with a partner. Talk about ways of making a box using Base 10 longs only.
* Now build all the different boxes you can from 8 longs. You may put the longs in 1 layer or in more than 1 layer.
• As you work, make a chart to record the length, width, and height of each box. Also record how many cubic units make up each box.
• How will you know when you have all the possible boxes? How can you prove it?
* Look for patterns in your chart.

Extension:
1. Challenge children to repeat the activity using 12 longs.
2. Ask children to use longs to build several different boxes, each with a volume of 200 cubic units.
Centers - * FasttMath on laptops
* open exploration Virtual Manipulatives - peg puzzle, towers of hanoi, etc

Assessments:
* teacher observations, various prisms, progress sheets, student-centered discussions, Base 10 longs
Materials:
* communicators, story, base 10 blocks, laptops

Tech Infusion:
Promethean board - flipchart, laptops

Accomodations/Modifications:
* teacher designed groups
* differentiated assignments/activities (centers to reach all levels)
* extended time-classwork/assessments(when needed)
* restructured homework assignments for both above level and below level students
* use of manipulatives/graphic organizers
* extension activities/alternative assignments
* organizational strategies - notebooks/book boxes/folder systems
* cloze-notes/study sheets/practice sheets for reinforcement
* modified assessments - M/C, SCR, ECR, O-E
* encouraging independence/student initiative
* includes a rich variety of resources, media ideas, methods and tasks
* personalized monitoring tools (checklists, goal sheets, thumbs up/down level understanding monitors)

Video Review - Workshop 2

In watching this video I found it interesting to see both the teachers and particularly Jeff getting frustrated by the question of how can you prove what you are saying. Like the video stated most teachers expect to attend workshops or trainings and learn some activities they can take back to their classrooms and be shown the right way of doing things. It is no surprise that there was some frustration in this particular situation - most trainings in schools weren't typically done in this manner of questioning and requiring the teachers to prove their thinking.

I feel very lucky in that our district has made a major move toward inquiry-based learning and we have been offered similar training in hands-on math through LLTeach (Paul Lawrence). This had been a slow process in getting everyone on board to this newer way of teaching math. Teachers see that although the basics are important for the students to learn, when the students are given these types of learning opportunities with manipulatives they can develop their higher order thinking while still reinforcing the basic operations.

Video Review - Workshop 1. Following Children's Ideas in Mathematics

After reviewing the video it made me realize how much more kids are capable of then we give them credit for sometimes. Unfortunately too many times we get caught up in the amount of content we need to cover to meet curricular demands and testing demands. It's easy to follow the textbook and work lesson by lesson and chapter test by chapter test. When kids are given the opportunity to explore it opens up a whole new way of thinking for them.

I have been teaching for 13 years and for many of those first years I found myself stressing out over not covering all the material that was written in the curriculum. At this point in my career I realize that although the curriculum and the NJCCCS standards are the guiding force in what you teach, it is my job to present my students with challenges and opportunities to meet these needs in creative, inquiry-based ways. I feel very fortunate that my district has had a strong push for inquiry-based instruction and PLC's in and out of the classrooms. We have received training from Paul Lawrence and utilize the Communicator Math programs. These experiences allow all students to explore more complex topics and ideas and develop their mathematical thinking.

Virtual Manipulatives Review 1

The virtual manipulative I chose to take a closer look at was Base Block Subtraction. It can be found in Grades 3-5 Number & Operations. Being a fourth grade teacher with students on varying levels (inclusion class) I found this manipulative to be very useful. I start our review of subtraction using the base 10 blocks and this is a great reinforcement activity. Students can create their own problems or there are some created for them. It models for them the process of subtraction with the bae 10 blocks. I have found that even though many of my students know the steps to subtract on paper, they have a difficult time using the hands on materials and an even harder time explaining what subtraction means and the actual process.

Having access to laptops and an interactive whiteboard in my classroom makes these virtual manipulatives an excellent resource for both reinforcement and enrichment.

4-story Towers

After finising up a math test in class, I posed the tower question to my group of fourth graders. I asked the students to predict how many four-story towers could be built using fifty of each of two colors of connecting cubes. Students recorded their predicitons on a lab sheet. Once the predictions were recorded, I instructed them to use the connecting cubes to build as many uniques four story towers as possible. As I walked around to see what the students were doing to solve this problems I witnessed many different things. Two groups split the towers of ten into towers of four of all the same color and one group seperated every cube and spread them out all over the desks. Another group I observed made two 4-story towers of the same color and then made 3-story one color towers and added the other colors to make the fourth story. They continued to take away the first color until they felt they had none left to change. The last group had over twenty towers, that of course were all the same color. I directed the students attention to the Promethean Board and revisited the original task. I reminded them that the towers needed to all be different. At that time the groups who were building many towers realized what was happening and started to pair up the towers they had built.
At the end of the lesson I asked each group how many towers they had. Many of the groups had 16 towers. Students recorded their towers onto the lab sheet and were given an opportunity to write why they think there were only 16 possible tower combinations. Students were very engaged and excited and asked if we could figure out how many towers they could build that are 5-stories tall. I assured them that we would continue the investigation this week in math centers.