Non-Routine Problems

The non-routine problem is a kind of unique problem solving which requires the application of skills, concept or principle which have been learned and mastered. It is also meant that whenever we are facing an unusual problem or situation which we don’t know the procedures to solve it, we are facing the non-routine problem.

Non-routine problem solving serves a different purpose than routine problem solving. While routine problem solving concerns solving problems that are useful for daily life (in the present or in the future), non-routine problem solving concerns that only indirectly. Non-routine problem solving is mostly concerned with developing students’ mathematical reasoning power and fostering the understanding that mathematics is a creative endeavor.

Non-routine problem solving can be seen as evoking an ‘I tried this and I tried that, and eureka, I finally figured it out.’ reaction. That involves a search for heuristics (strategies seeking to discover). There is no convenient model or solution path that is readily available to apply to solving a problem. That is in sharp contrast to routine problem solving where there are readily identifiable models (the meanings of the arithmetic operations and the associated templates) to apply to problem situations.

Tangram Activities!

Classroom Puzzles (K-2)

Prepare sets of tangrams for your students ahead of time. You should make 2 sets for each student. Explain a little of the history of tangrams and show your students some of the many pictures that can be made.

Challenge your students to create their own designs with their tangrams. Can they make a fish? A cat? A strange-looking plant? When students have had opportunity to explore and create, have them create their favorite design and then glue the arrangement onto construction paper. Later, when the glue has dried, use these designs as a classroom set of puzzles. Hand out the designs and new sets of tangrams and have students try to recreate their classmates’ designs. With younger students, the designs may be recreated by matching the pieces directly on top of the puzzles. After the activity, use the puzzles to decorate your classroom.

Fun maths activities!

Maths Graphing Activities in Classroom.....

There are many fun elementary math graphing activities you can use to teach your first graders about graphing. Start with making concrete graphs and then move to picture graphs to give your students a good foundation for graphing.

Elementary Math Graphing Activities

Before they can learn to interpret and use graphs, students need experience with making their own. Younger students will understand graphing best when they begin graphing using real objects. After they have experience with real graphs they can begin to make picture graphs and symbolic graphs.
Try these ideas for making concrete and picture graphs. You can purchase a pre-made floor mat for graphing or make your own using a white shower curtain liner and making a grid on it with painter's tape.
After you complete each graph let the students talk about their observations and then ask questions about the graph. Some questions to consider are:

• Which column has the most? the least?
• Are any columns the same?
• How many _________?
• Are their more _________ or more ________?
• How many more __________are there than _________?
• How many fewer ____________ are their than ___________?
• How many are their altogether?

Elementary Math Graphing Activities: Real Graphs

Shoe Graph
This is an easy first graphing experience for students. Have each student take off one shoe. Sort the shoes into piles for laces and no laces. Then label two columns of your floor mat Laces and No Laces with index cards. Have the students line that shoes up in the appropriate columns and then discuss the graph. They may need some guidance deciding where to place the shoes, if this is their first time graphing. You can also graphs shoes by color or type of shoe e.g. boots, sneakers or sandals.

Apple Graphs
If you teach kindergarten or first grade, you probably have an apple unit early in the year. To add some graphing to the unit, have each student bring in a red, yellow or green apple and then sort and graph them onto your graphing mat. You might bring in one or two yellow and greens, so that you don't end up with all red apples and so that you have extra for those who have forgotten to bring one. After you graph you can use the apples for tasting the different colors or for making applesauce. If you do apple tasting, have each students draw his favorite color apple onto an index card and then graph the favorites. This is a great transition to a picture graph.

Candy Graphing
Make a graphing mat for each student on white paper. Then give them m&m's, skittles, gummy bears or lifesavers to graph by color. Near Valentine's Day, give each student a box of conversation hearts to graph. They can lay the candy pieces into the squares in the columns for each color. To extend the activity, have them color in the squares to make a bar graph after they have made the real graph.
Other fun foods to graph and eat are Fruit Loops or Trix cereal, small boxes of animal crackers and colored goldfish crackers.

Picture Graphs

Once your students have mastered making graphs with real objects, start letting them make picture graphs. You can use your floor mat or just tape their pictures to chart paper or the chalk board.

Graphing Favorites
Favorites are easy for young children to graph. You decide which items they are going to choose from so that you don't end up with too many columns. If you are graphing favorite pets, give them the choices dog, cat, bird or fish. Someone will probably insist that his favorite pet is a snake, but you can just tell him to choose his favorite from the choices given. Then have each student draw a picture of her favorite and place it on the graph.

Other favorites to graph:

• Shape
• Color
• Type of weather
• Holiday
• Ice Cream Flavor
• Type of fruit or vegetable

Weather Graphs
You can keep an ongoing weather graph each month to track what the weather is like. Make pictures of a sun, clouds, rain, snow and wind and add one to your graph each day to represent the weather after your class has been outside. During a weather unit, you might want to actually take a picture outside each day to show the weather and then use the picture to make a graph at the end of your unit.

Lunch Graphs

If you are required to send in a lunch count each day, you can make it a daily graphing activity. Just make a bunch of die-cuts of lunchboxes and a dollar sign or something else to represent buying lunch. Have your students graph the picture that tells what they will be doing for lunch each day when they arrive at school. You can also laminate a graph with columns for buying lunch or bringing lunch from home on it and have each student place his picture in the appropriate column each day. This works as an attendance graph too, because you will be able to see which students picture are not on the graph. Discuss the graphs as part of your morning calendar time.
These fun activities will help your students become experts at graphing!

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Fun games to play in geometry class!

Looking for a fun way to spice up your geometry class while still learning? These geometry games are a great way to review shapes, area, and perimeter.

Shape Bingo or Matching

For younger kids, try using a variation of the classic game of Bingo to teach them their shapes. Cut out shapes and have students glue different shapes to premade Bingo boards. Make sure that they only have one of each shape. Then call out the name of a shape, and encourage students to place a marker on that shape on their board. For very young students, use shapes such as square, circle, triangle, or rectangle. For older students learning more complex geometric concepts, you can use terms like obtuse angle, parallelogram, trapezoid, and right triangle.

A different way to review the concept of shapes is to create a matching game. This will only work with students who can read well, but it can be used for older students as well. Simply have students draw a shape on one square and write the name of the shape on another square. Then have them turn the squares upside down and play a normal game of matching, with a match being the shape and its name.

 

Geometry Walk

 

Take students on a geometry walk in your school building or outside. Divide students into teams, and bring along a stack of sticky notes for each team. Have students point out objects that they see that have various shapes, and draw each one on a sticky note. When you return to the classroom, have students discuss their findings with the class by posting the sticky notes on the board and reading through them.

Match the Area or Perimeter

Tell students that they are all designers in charge of designing unique potato chips for a famous chip company. Explain that the chip company has only one requirement: all of the chips must have either an area of 24 or a perimeter of 20. Divide the class into groups, and tell them that each group is competing to come up with the most possible chips that can be designed for the company, but that they only have five minutes to come up with as many as they can. Hand out a stack of sticky notes to each group and set the timer. When they finish, have each group attach their sticky notes to the board in a different area. Encourage students to check their classmates’ work to make sure that they all either have the given perimeter or the given area.
Try some of these geometry games the next time you find your students nodding off. They’ll love applying what they’ve learned in these fun ways.