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Mrs. Leach |
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Online Resource LibraryOnline Resource Library by Denise Leach CEP 805 This is a collection of online resources that can be used for the teaching The Techonology Principle of the NCTM states “Technology is essential in teaching and learning mathematics; it influences the mathematics that is taught and enhances students' learning.”
This is a great resource for teachers, parents and students. Resources are organized alphabetically by mathematic subjects. Teachers can view NCTM goals and affordances of technology for each resource. Parents and students can click on blue titles and go directly to the activities. NCTM Goals for grades 3-5
NCTM Goals for grades 3-5
Color Patterns (group evaluation reformatted by Jodi LePla) Description This activity has students watching a pattern of dots be created. The student gets to continue the pattern on by clicking on the color choices. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? This addresses three of goals of the NCTM's Algebra standard
What is the nature of the mathematics? Students are given the beginning of a color pattern and have to fill in the remaining spaces with the correct colors. Students must understand patterns, analyze the pattern in order to complete it correctly, and use the model to continue mathematical thinking. It's a way of doing algebra with pictures, not numbers. Students can recognize, describe and extend color patterns and sequences. 2. How does learning take place? After students have filled in the remaining colors, they click on 'check answer.' The computer tells them if they are correct or if they should try again. The immediate feedback allows for errors to be corrected right away. The learning is the completion of the pattern. Students must physically complete the pattern, and it is assumed the student will fix errors through analyzing the pattern, not substituting new colors until it is correct. 3. What role does technology play? This resource automates working with patterns, making it interactive and simple for the user. The technology provides instant feedback, requiring students to enter the pattern correctly based on their predictions for the pattern. If done in pairs this allows the students to reason with the answers, explain patterns, and work together to solve patterns. This offers students an opportunity to extend patterns easily with immediate feedback. This also provides an additional representation of color patterns and finishing the sequence. It provides the opportunity for discussion and reinforces different ways of algebraic knowledge and thinking. The sound effects are engaging and motivating for students without being distracting. 4. How does it fit within existing school curriculum? This allows students to find patterns, and then complete the patterns. It supplements our curriculum of working with patterns in elementary school. It enhances the work students do with patterns and provides a new resource/arena for students to practice in. It enhances students learning and thinking about sequential relationships. It also allows for teachers to give a quick review or practice time to this skill. Return to TOP
Displaying Number Patterns (group evaluation reformatted by Denise Leach) Description This is an E-Example offered on the NCTM website to address the Algebra Standard in primary grades. It provides a visual way of highlighting and displaying various patterns and relationships among numbers with a hundred chart and calculator screen. It describes the goals it addresses and a task for students. It also has links to another activity to extend the patterns beyond 100. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? This addresses all four of the goals of the NCTM Algebra standard
What is the nature of the mathematics? This activity allows students to explore number patterns by punching numbers into a calculator (for example, to skip- counting by 5s, the students would punch in 5 + 5 =, =, =. The answers show up on the calculator screen and also are highlighted on a hundreds chart next to the calculator. More than one pattern can be displayed on the hundreds chart at a time, which is a nice feature. 2. How does learning take place? In a primary classroom, the teacher would probably have to lead this activity unless the students had already had lots of previous experience with exploring number patterns on a calculator and hundreds chart. The teacher could have students predict what would come next in the pattern before pressing the = button, for example. Then discussion could take place about the pattern. I think this could be considered constructive learning, since students could be exploring whether their predictions are correct and constructing their own learning. This applet allows students to begin to use variables and algebraic expression as they describe and extend patterns. Students can also notice patterns with odd and even numbers. 3. What role does technology play?
The technology in this activity, like a regular calculator, makes skip-counting or exploring other number patterns simpler. The hundreds chart feature helps to represent the knowledge. Students can use the information to communicate about what they are learning about the relationships between numbers. This applet allows two more ways to show how numbers are related. Repeated addition on the calculator and the pattern on a hundreds chart. The hundreds chart allows students to see the patterns--vertically, horizontally, diagonally, etc. 4. How does it fit within existing school curriculum? This fits into any existing curriculum as a way to use technology to show skip counting and repeated addition. This lays the foundation for multiplication. This activity could be used to introduce number patterns, reinforce thinking, re-mediate, or extend thinking. It really could be used for so many things! It is a great tool to give a visual to number pattern lessons at the primary level. Return to TOP
Pattern Generator (group evaluation reformatted by Denise Leach) Description The Pattern Generator allows students to complete patterns by dragging in shapes from a sidebar. Students must understand the visual pattern and analyze the change of each shape's location. Students recognize, describe and extend patterns such as sequences of shapes and objects. It is an interactive board that allows students to change the difficulty level and reset the board to explore different patterns. There are tabs that provide more instruction and information for learners and instructors. Worksheets to accompany the activity can be accessed. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? This addresses three of goals of the NCTM's Algebra standard
What is the nature of the mathematics? As students create patterns they must understand the visual pattern and analyze the change of each shape's location. Students recognize, describe and extend patterns such as sequences of shapes and objects. 2. How does learning take place? To quote the "help" section of the site, "If the correct piece is placed, it will remain on the board. If an incorrect choice is made, the piece will not show on the board. When this happens, [students] select another piece to place on the board, and take a second look to try to figure out the pattern." This gives students immediate feedback on their work. Students are shown the beginning of the pattern and are given enough objects to continue the pattern. They are different objects used for the pattern. 3. What role does technology play? The technology simplifies the task of continuing the pattern and receiving an answer of whether the answers were right. Knowledge is represented through the pictures. If this activity is used for partner or group work, students could collaborate and discuss how they found and continued the patterns. There is even discussion questions included in the site under the "Instructor" tab. The site allows differentiation with different difficulty levels. This meets the needs all students, supporting strugglers while offering challenges to others. This model best affords communicating and collaborating and representing knowledge and thinking. If done as a whole group or small groups, students can collaborate to finish the patterns. It also reinforces finishing patterns and higher level thinking as the difficulty levels increase. 4. How does it fit within existing school curriculum? This resource would be used to supplement curriculum by providing a means of practicing patterns. It could be used as work with patterns, or it could be used to introduce a new concept of writing expressions from patterns, e.g. n+2. I think it'd be best used as practice problem solving to find patterns. It also provides a fast and manageable way for teachers to allow students to practice patterns. Return to TOP
Poddle Weigh-In (added by Jodi LePla) Description This game introduces students to the concept of variables. They describe it as “something can be a ‘container’ for a number. The poddles have lost the numbers that usually show up on their shirts. By placing each poddle on a scale and adding weights, the player can determine what number the poddle is. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? NCTM Standards: Algebraic Thinking Grades 3-5
What is the nature of the mathematics? Students learn that they can use an equation (a statement that two different expressions are equal to each other) to find unknown values that make the equation true. 2. How does learning take place? Students add weights to the scale to balance or equalize the scale. Each time they add a weight the scale moves. Students have weights that weigh 1, 2, 3, and 4 pounds. If you go over, you can take away a weight and try a lower weight. 3. What role does technology play? The technology is engaging and fun. Students can work together or independently to balance the scales.
4. How does it fit within existing school curriculum? This would fit into any elementary school curriculum to supplement equation lessons. 5. How does the technology fit or interact with the social context of learning? Students could work together to discuss which weight is needed to balance the scale. 6. How are important differences among learners taken into account? This is a great activity for visual learners. Students can see how each weight affects the scale. Students do not have to do any calculations or write numbers down. They can experiment in a safe environment. Return to TOP
NCTM Goals for grades 3–5
Farm Animal Pictogram (submitted by Angie FitzGerald) This resource is an interactive web page in which students can explore creating a pictogram. Students can gather data and then create a pictogram by adding a title and descriptions to the web page, and then adding pictures so the pictogram shows what their data says. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? NCTM:
What is the nature of the mathematics? Students have to understand that one picture means one unit, and they have to understand what data they are collecting. 2. How does learning take place? Students create graphs from data they have. They must manipulate the graph so that the graph looks the way they want it to. 3. What role does technology play?
4. How does it fit within existing school curriculum? This would be intended to supplement existing curriculum. It would be a good practice once students understand the basic concepts of what a pictogram is. Return to TOP
Plop It! (added by Jodi LePla) Description This activity allows the user to experiment with mean, medium, and mode by using a bar graph. This activity would work well in groups of two or three for about 25-30 minutes if you use the exploration questions and 5-10 minutes otherwise. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? NCTM Standards: Data Analysis and Probability Grades 3-5
Grades 9-12
What is the nature of the mathematics? Mean, median, and mode 2. How does learning take place? Students take data they have collected or are given and input them into the work space. As students enter the data, they can see their graph form. Markers across the bottom show the mean, median, and mode. This changes as the students update the graph. Students are able to see how each piece of data impacts the mean, median, and more. 3. What role does technology play? The technology helps students focus on the connection between the data set and the mean, median, and mode. The technology shows students how these can change as new data is entered.
4. How does it fit within existing school curriculum? Beginning in the 2nd grade students begin to look at data and analyze it. This applet lets students see the connections without the distraction or coloring in the graph or recalculating the mean, median, or mode when new data is obtained. 5. How does the technology fit or interact with the social context of learning? This activity would be great to use in small groups. Students would be able to make predictions about changes to the graph when new data is entered. They can discuss why the mean, median, or mode changes or doesn’t change with each piece of new data. 6. How are important differences among learners taken into account? This is a great activity for visual learners. Some students may not be able to calculate mean, median, and mode independently. This activity would allow any student to input their data and have a graph with useable information quickly. Their work would look like their classmates and would support their learning and understanding of these concepts. 7. What do teachers and learners need to know? Students or teachers should have data sets available. There is a help page for definitions and extended activities on the instructor page. Return to TOP Bobbie Bear added by Denise Leach Bobbie Bear is an activity that addresses the NCTM Standard for Data and Probability grades 3-5. Students should be able to · formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them; · select and use appropriate statistical methods to analyze data; · develop and evaluate inferences and predictions that are based on data; · understand and apply basic concepts of probability. Bobbie is going on vacation and wants to know how many outfits he can make out of the articles of clothing in his closet. As students change his clothes the outfits are displayed. When they have used all possible combinations the closet closes and they are told he is ready to go on vacation. If they choose the same outfit they get immediate feedback telling them they already have that one. The number of shirts and pants can be increased and continued playing allows students to see the relationship between the number of clothing articles and outfit choices. This basic concept is show in a concrete real life way that allows students to make inferences and predictions based on data. There is a link to a lesson plan to use with this activity that includes follow up questions and extensions. It is user friendly and very engaging. Return to TOP
Spinners - Marissa Snodgress This virtual manipulative can be used to teach about chance and random choices. You may spin the spinner, change spinner regions (Name, Color, and Size), and record results from multiple spins. A region's name can be edited to give it a name to match it with the things being chosen, such as people, toys, or foods. Changing colors in each section will be helpful to identify the regions on the spinner. A student can also change the size of each region, and, therefore, change the probability that a region is selected by the spinner. The results of the spins can be tallied and combined with any earlier results. This will be shown as a histogram. This is interactive and lets students have a hand in analyzing data and figuring probability. It would be great as a whole class activity or in student groups. There is immediate feedback and it allows students to track the results over time. Return to TOP
NCTM Goals for 3-5
Platonic Solids (added by Denise Leach) Description This is a virtual manipulative that shows a platonic shape that can be rotated and re-sized. As students select vertices, edges, and faces the program marks them and counts their totals which are displayed. Euler's formula is shown and students can observe that the number of vertices minus the number of edges plus the number of faces is always equal to 2. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? Two of the goals for the Geometry Standard are addressed
What is the nature of the mathematics? Students identify and classify familiar three dimensional solids. As they mark and count faces, vertices and edges they are labeling component parts of solids. They are viewing front, top and sides of solids as they move the shape around. 2. How does learning take place? As students mark faces, edges and vertices they are identifying the component part. They are able to rotate the shape and observe it from all views and verify totals shown. 3. What role does technology play? Using this technology allows students access to information. Platonic solids are defined, geometry vocabulary is used to describe component parts, and an explanation of Euler's formula is given. This activity automizes, simplifies and transforms the task of labeling, identifying and counting component parts of solids. It allows students to highlight, rotate and manipulate shapes virtually without the use of a physical object and represents knowledge and thinking of an abstract idea. Using this technology allows students the access to these virtual manipulatives so that they can communicate and collaborate with peers. 4. How does it fit within existing school curriculum? This activity addresses the Geometry Standard for third grade. The grade level expectation is that students will be able to identify, describe, build, and classify familiar three dimensional solids. Teaching of geometry should include various exposures to three dimensional solids such as concrete examples, nets and descriptions in textbooks. Using the virtual manipulatives will enhance teaching of the geometry standard by making abstract ideas more visual. 5. How are important differences among learners taken into account? This activity allows students to work at different levels of ability. It offers a visual representation of abstract concepts (how many faces, vertices, and edges) for students that need more work identifying these component parts. It also exposes students to Euler's formula that the will apply to future work in geometry and algebra. Return to TOP
Shape Tool (added by Jodi LePla) Description This tool from Illuminations allows students to create any geometric shape and then color, enlarge, shrink, reflect, slice, or glue them together. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? NCTM Standards: Geometry
What is the nature of the mathematics? Students are exploring with the shapes to learn about flips, turns, and rotations. Students will also be learning how to recognize and create shapes that have symmetry. 2. How does learning take place? Students learn geometry by exploring the different shapes. They can move the shapes any place on the canvas. They can change the size if needed to make it fit. They can explore the reflect button and the tool shows the reflection. Students can undo this move and it goes back to the original position. The creators of this tool assume that students know their shapes. They may assume that students know the vocabulary words: reflection, tessellation, rotate, and mirror. This vocabulary should be reviewed by the teacher to make sure students understand what happens when they push that button. This tool will reinforce the concepts. 3. What role does technology play? Technology supports student learning and understanding of geometry. Students will learn about symmetry when they make their pattern and click on the “”mirror” button. They immediately get to see the mirror imager, quickly and correctly. Students can represent their learning by creating tessellations. I think this tool can transform learning because it makes this concept very concrete and visual for students. They can immediately see the affect of clicking on one of the rotate or flip buttons. They can easily see the mirror image. This will lead to them being able to mentally flip and rotate in their minds. Students could put a shape on the canvas, predict what it will look like when they rotate it and then check to see if their prediction was true. I think this tool can easily be used for collaboration and communication. Students can work together to create tessellations or patterns. Once the class has tried to solve the problems they can come back as a group to discuss what they found. Students could then discuss why some shapes work and others didn’t. They could easily use a SmartBoard to demonstrate to the class their thinking. 4. How does it fit within existing school curriculum? This applet fits into any math curriculum. It supports student learning of manipulating shapes and learning about their properties. This is a great tool to foster students’ ability to use visualization and spatial reasoning. 5. How does the technology fit or interact with the social context of learning? Students could work together to predict what will happen if they click on the different buttons. There are different explorations to complete that would be ideal for partners or groups of three to test out. Return to TOP Geo Cleo and the Shape Caper - Angela FitzGerald Ladybug Maze Marissa Snodgress Transformations-Reflection Tool - Angela FitzGerald NCTM Goals for grades 3-5
Coins for Candy (submitted by Angie FitzGerald) This is a web-based lesson that walks students through the identification of coins--pennies, nickels, and dimes. It covers coin identification, coin value, and different ways to make an amount. Students must interact with the lesson by clicking on the correct coins. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed?
What is the nature of the mathematics?
2. How does learning take place? This is an interactive web lesson. Students are presented with a situation in which a little girl cannot go to the candy store until she learns about coins. Students are presented with information about pennies, nickels, and dimes. They have to click on the correct coins in order to move through the lesson. The lesson has built-in feedback based on what the students click. After learning how to identify the coins and their worth, students practice what they would have to do at the candy store and choose the correct group of coins based on the price of the candy. 3. What role does technology play?
4. How does it fit within existing school curriculum? Being able to identify money is a very important concept that is an essential life skill. This lesson could be used to introduce the penny, nickel, and dime, but would probably be better used as a reinforcing lesson after those three coins have been taught in the classroom. It could also be a remediation lesson for struggling students. 5. How does the technology fit or interact with the social context of learning? Computers could be used by individuals or in pairs to work on this lesson. Students could communicate to come up with an agreed-upon answer to the questions presented. The computer gives feedback based on the answers chosen. 6. How are important differences among learners taken into account? The feedback given by the computer is different for different answers given. If a wrong answer is chosen, the computer gives hints as to how to get the correct answer. Return to TOP What Time Is It? (Marissa Snodgress) Description This applet allows the student to predict a new time when given a certain length of time that has passed. It requires the participant to use both a digital and a face clock. The first questions are easy, predicting the time change 20 minutes from the given time. For example, the first clock will show 3:40pm. It will ask the students to manipulate the time on the second clock to show what time it will be in 17 minutes. As the problems are answered correctly, they become more and more challenging. It asks the student to change hours, minutes, and seconds. They are working with a base-60 and base-12 number scale (for minutes and hours that pass). Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? NCTM Measurement Grades 3-5:
What is the nature of the mathematics?
2. How does learning take place? It is assumed that by using this resource students are building their fluency and understanding of working with elapsed time by adding to their background knowledge of predicting elapsed time. This applet requires knowledge of working with time before being able to complete it successfully. It is also assumed that students learn best with instant feedback and repetition of computation. 3. What role does technology play? In this applet, technology has two main roles in the learning process.
4. How does it fit within existing school curriculum? This resource is to supplement previously learned math connected with telling time. It is a great practice for students to predict elapsed time and work with a number system that's not base-10. It does not teach any new material, but it does allow reinforcement of working with time. It provides a place for students to become stronger with a concept they often struggle with. 5. How does the technology fit or interact with the social context of learning? This technology could be used on an individual basis or in collaborative groups. It can be completed by one student, or pairs could work together to predict and justify their answers. They are then given immediate feedback on their results - allowing for further learning with more challenging material or a chance to find their mistake. This requires students to verbally explain their math processes in a problem - something that can be difficult for some students. 6. How are important differences among learners taken into account? This applet allows students to work at their own pace. Only after multiple correct answers do the problems become more difficult. Therefore, learners can progress at their own rate and work on problems that are just right for them. Return to TOP Fill and Pour - Marissa Snodgress The Ruler Game is an activity that address the NCTM Standard for Measurement for grades 3-5.
The opening screen is a ruler. Students play a game of identifying the increment given on the ruler. If they are correct they continue playing. If they guess wrong they receive immediate feedback of the right answer. They can change the preferences to make the game more difficult. They can choose increments of whole, halves, quarters, eighths or sixteenths. After three strikes/mistakes you’re out. The page answers the question Why Learn to Read a Ruler and gives instructions on how to play the game. It also has links for purchasing real rulers. This provides a visual representation of a ruler and the basic units of measurement. Return to TOP
NCTM Goals for grades 3-5
Count the Money (Added by Jodi) Description This game is all about counting money, There are three different levels: How Much Money is There?; Exact Amount; and Make a Dollar. Real images of money are shown and the amount is given to support learners. Evaluation (evaluate the resource by responding to the focusing questions; questions 1-4 are required for all resources. Use questions 5-7 as appropriate. You should include at least one of questions 5-7 for each resource, but you don't have to include them all.) 1. What mathematics is (potentially) being learned? Standard(s) addressed? Understand numbers Understand operations Compute fluently What is the nature of the mathematics? Whole Numbers Place value Addition 2. How does learning take place? Students are able to practice counting money as much as they need it. This activity offers many examples with immediate feedback. All of the materials needed are available, so students don't have to worry about running out. 3. What role does technology play? Technology provides a fun and engaging way to practice counting money. This applet offers fast feedback and quickly moves to the next problem. Students are able to drag the coins needed onto the "canvas". It is a quiet activity. 4. How does it fit within existing school curriculum? Money is an important skill at all grade levels. This applet fits right into the math curriculum. 5. How does the technology fit or interact with the social context of learning? Students need exposure and a lot of practice to be able to understand and use money. This applet offers another way teachers can let students practice this skill. This can be an independent activity, a partner activity, or done with a group of students at the SmartBoard. Students can share their counting strategies and their thinking. One student could solve the problem and another student could show it a different way, with less coins perhaps. 6. How are important differences among learners taken into account? Actual money is shown on the screen. The amounts of each coin are also shown to support students who are still learning to recognize coins and their value. There are three different levels, so students can work where they are at. Return to TOP Diffy - N&O Page: (Marissa Snodgress) Description This is a set of inlaid squares. Students must complete the four subtraction problems on each side of the square before moving to the next square. When the four outside circles have all been filled correctly, blanks will appear in circles in the next inner square. Students continue filling in the blanks until they complete all the squares. Students can choose new problems and the computer will give them another starting set of black numbers. Students (or teachers) can click Create Problem and enter any set of four black numbers for the outside square. Evaluation 1. What mathematics is (potentially) being learned? This applet asks students to practice their knowledge of operations, mainly subtraction. They must compute their work fluently to progress through the applet to get to the center square. They may subtract whole numbers, integers, fractions, decimals and money. Students work with whole numbers, place value, fractions, and subtraction. Standard(s) addressed? NCTM Numbers & Operations Grades 3-5 What is the nature of the mathematics?
2. How does learning take place? Students are learning to work with fractions, thus requiring them to learn about whole numbers and their relationships to fractions. They mainly learning how multiplying fractions takes place with an interactive grid as guidance. Students can see, as they make the fraction values in the table, the shaded part that both fractions share is the answer, but the number of squares changes and it changes the denominator. 3. What role does technology play? This applet is virtual manipulative designed to stimulate student practice of subtraction. There is instant feedback and the site is visually appealing to students when completing their problems. Students are even given the chance to make their own problem which encourages a higher level of thinking. In this applet, technology has to main roles in the learning process.
4. How does it fit within existing school curriculum? This resource is to supplement current curriculum. It allows students to practice subtraction and addition with decimals, integers, and money values. It is practice to allow the process of subtraction, and therefore addition, to become more fluid for students. This strengthens their knowledge base as they enter higher level mathematics. 5. How are important differences among learners taken into account? The site allows the teacher or student to pick which process will be used and practiced. The set up of the math is intriguing enough to students for them to look at the patterns that solved the squares and to try again. It also has varied levels to reach different levels of learners. This technology allows a student or teacher to create their own set of problems, which can challenge higher-level learners. Return to TOP Multiplication of Fractions (Marissa Snodgress) Description This virtual manipulative graphically demonstrates, explores, and allows practice in multiplying fractions. There is a grid that shows two fractions multiplied together - showing one fraction in red on the left and another in blue on the bottom of a grid. The area of the overlapping squares, shown in purple, is the product of the fractions. There are equations to the right of the grid that show the same product that is colored on the grid. A student can change the numerators of the fractions by dragging the sliding tabs. To change the denominators of the multiplied fractions students click on the up and down arrow. The array, or area model, is quite effective when illustrating multiplication of two rational numbers (fractions, decimals, percents, or some combination). Evaluation 1. What mathematics is (potentially) being learned? This applet asks students to practice their knowledge of operations, mainly subtraction. They must compute their work fluently to progress through the applet to get to the center square. They may subtract whole numbers, integers, fractions, decimals and money. Standard(s) addressed? NCTM - Numbers & Operations Grades 3-5 What is the nature of the mathematics?
2. How does learning take place? Students are learning to work with fractions, thus requiring them to learn about whole numbers and their relationships to fractions. They mainly learning how multiplying fractions takes place with an interactive grid as guidance. Students can see, as they make the fraction values in the table, the shaded part that both fractions share is the answer, but the number of squares changes and it changes the denominator. 3. What role does technology play? This technology affords the student a chance to learn how to multiply fractions, with a written resource of how it works. the grid automates the multiplication and simplifies the process. It is easier to manipulate the grid, rather than do the problem by hand with numbers. It shows a different way to think of fractions and their relationship in multiplication. Student’s answers represent knowledge and thinking. If the answer is wrong the student has to find the correct answer before moving on. If the answer is correct there is instant feedback with a written explanation of why the answer is correct The grid makes it quite easy to correctly answer the problem, giving a chance for them to look as to why it was correct. In this applet, technology has to main roles in the learning process.
4. How does it fit within existing school curriculum? This technology is intended to supplement existing curriculum. It is intended to enhance the learning of a concept already central to the curriculum by providing repetitive practice for learners. It is a visual representation of multiplying fractions. This resource is an aid for a content area that can be difficult for elementary students (and even middle school learners). It is very interactive and students can see how products vary depending on the change in fractions. It also provides practice with immediate feedback; something that is hard for teachers to provide on a constant basis for each student. Return to TOP
How Multiplying Works (added by Denise Leach) Description This is a step by step visual explanation of multiplication. It asks the viewer to interact by drawing answers before the answer is revealed. It provides pictures to help students understand the meaning "groups of". As they work through the explanation they receive immediate feedback when the correct answer is revealed. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? This addresses two of the goals of the NCTM Numbers and Operations Standard
What is the nature of the mathematics? Students are given a visual and written explanation of how multiplication works combining like groups. First they read through the explanations and view several examples. As they work through each page they are guided to predict what the answer will be. The correct answer is revealed providing immediate feedback. 2. How does learning take place? The instructions are displayed and the viewer is asked to interact. Answers are hidden until the mouse rolls over a specific area. Groups are shown individually and combined to provide a visual representation of multiplication. 3. What role does technology play? This program provides access to information in a description of multiplication. It also represents knowledge and thinking with visual representations of groups being formed and joined together. It also allows the viewer to show their thinking by trying to solve the problems before revealing the answer. If done in groups or partners it would offer an opportunity to communicate and collaborate with peers. 4. How does it fit within existing school curriculum? Students in 3rd grade need to begin making connections between repeated addition and multiplication. They are supposed to understand "How many groups?" and "How many in a group?" The possibilities for use of this activity are numerous. This could be an introduction to multiplication offering a step by step explanation. It could also be used to re-teach the concept if a student did not understand the concept as it was presented a different way. It could also be an extension for students in lower elementary grades that are ready to move ahead. 5. How does the technology fit or interact with the social context of learning? This activity allows students to work individually or as a partner/group to read through the explanation. It also allows them to interact and discover correct answers with immediate feedback. Return to TOP How to subtract by regrouping? (added by Denise Leach) Description This is a video that begins by showing and telling step by step how to subtract a two digit number with regrouping using base ten blocks and an algorithm. Then it repeats the steps to show how to solve a three digit number. As it describes regrouping the steps are highlighted with a pointer n the screen. Base ten locks are broken into smaller pieces to show regrouping and numbers are drawn in the algorithm to show how these ideas are connected. The video is teaching how to regroup. Through the use of several models a narrator explains each step. How to regroup is shown using base ten blocks and with numbers. The explanation also points out the place value position of each number in the problem. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? It addresses three of the goals of the NCTM Numbers and Operations standard
What is the nature of the mathematics? Students listen to explanation and see visual representations of subtraction with regrouping. 2. How does learning take place? The video is explicitly teaching how to regroup. Through the use of several models a narrator explains each step. Regrouping is shown using base ten blocks and an algorithm. An implicit connection between the base ten blocks and the algorithm is shown. The explanation also points out the place value position of each number in the problem. 3. What role does technology play? This explanation provides access to information as regrouping is described. It shows step by step how to transform a number in order to regroup. The thinking involved is described by the narrator. 4. How does it fit within existing school curriculum? I think this could be used to supplement lessons on regrouping. Students that have difficulty understanding the algorithm can watch the video for another presentation of the concept. They can also stop the video and go back to repeat the explanation whenever they need to. 5. How does the technology fit or interact with the social context of learning? This activity allows the student to work individually to receive step by step instructions on how to regroup. This could also help parents trying to assist with homework. Base ten representations may not have been used when parents were in school. This helps them understand the connection of these manipulatives to regrouping. Return to TOP Math Mysteries (added by Jodi) Description This website allows students to choose from two different characters. Each character has different mathematical problems to be solved. The character models and explains how to solve a similar problem and then the student is given the chance to work on it themselves. Students practice the skill 2-3 times before moving on to the next problem. Evaluation 1. What mathematics is (potentially) being learned? Standard(s) addressed? Understand Numbers Understand Operations Compute Fluently What is the nature of the mathematics? Whole numbers Place value Fractions Addition Subtraction Multiplication Division 2. How does learning take place? Students interact with the computer solve different problems. The problem is modeled for them and they are given 2-3 different problems to solve in a similar manner. Students are engaged in the fun and interesting lessons. 3. What role does technology play? The technology makes learning fun and engaging. Students have to solve an actual problem and not just compute numbers for an answer. Technology makes concepts more concrete and visual. The symmetry game is very visual and is easy to manipulate. This site hits on the following affordances of technology: automating, simplifying, and transforming tasks; and representing knowledge and thinking. 4. How does it fit within existing school curriculum? This technology would be a great supplement to any math curriculum. Its main focus is on problem solving. Students are working on before and after, expanded notation, fractions, and patterns and symmetry. 5. How does the technology fit or interact with the social context of learning? This activity can be done independently or with a partner. Students could discuss how they solved the problem and the strategies that they used. This could also be used as an extension activity if you taught lower elementary but had a student that needed more of a challenge. Return to TOP Number Line Arithmetic by Angie FitzGerald Standard(s) addressed? NCTM understand numbers, ways of representing numbers, relationships among numbers, and number systems; understand meanings of operations and how they relate to one another; Users can choose addition, subtraction, multiplication, or division problems for the number line to show. It only works with whole numbers. 2. How does learning take place? 3. What role does technology play? 4. How does it fit within existing school curriculum? 5. How does the technology fit or interact with the social context of learning? |
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