Tag Archives: measurement

Math Myths

Spring 2010 277Since so many teachers are fearful of math, I am going to start out by exploding some of the more common myths that prevent us from thinking mathematically and actually ENJOYING teaching it!

Myth 1: Math is about getting the one right answer. No matter what you experienced in math class this is not correct. Truth: Math is about finding an answer that everyone agrees on.

Myth 2: Math is about numbers. Numbers are one of many tools that mathematicians use to solve problems. They also use objects and symbols and words and pictures. So then what is math? Truth: Much of mathematical thinking is devoted to the search for patterns and and solutions to problems describing those discoveries in ways that others can understand.

Myth 3: Math is boring. Truth: Math when taught properly can be just as fun as the arts. In fact, when I asked my third grade classes to vote on their favorite subject, they always chose math. But then why wouldn’t they when we had a six foot blue frog who was the king of the kingdom of three, they got to use chopsticks in a paper ball race and earned wages making products for their class store that they then sold to raise enough money to go to the Syracuse Zoo.

So how do we combat those myths and teach math so kids love it?

Make it meaningful! Counting, adding, and filling in worksheets because the teacher tells you to is a surefire way to bore children to death. Instead, always give them a purpose for thinking mathematically. Some examples:

  • Counting and computing for a purpose:  If you are addressing a common core math standard such as this one for kindergarten: K.C.C.A.3 Write numbers from 0 to 20. Represent a number of objects with a written numeral 0-20 (with 0 representing a count of no objects), don’t take it at face value and give the children a worksheet with a picture of 3 apples and a space for them to write the number 3. Instead, think of a reason why they might want to count something and record the number.  Bring in a basket of crackers for snack. Make a chart for them to write their name and the number of crackers between 3 and 6 they want for their snack. As they gain experience make it more challenging. Bring in two or three different types and have them record the number of each kind they want and the total which cannot be more that 8, for example. 
  • Buying and selling: The class store using play money is a tried-and-true method used by teachers for decades for getting children to practice adding, subtracting, and more. In addition to a store think of other places money is used and set up dramatic play centers such as restaurants, plant nurseries, even an art gallery where children can buy things from each other.
  • Earning money for a purpose: Even better is raising or collecting money for a real purpose like our trip to the zoo. One time our school collected pennies for charity and the classes had to come up with different ways to count the huge jars of pennies turned in.
  • Being mathematically curious: Math is about comparing things and finding patterns. Ask which is bigger/longer/more? How do you know? Invite children to find and make patterns: Look at the interesting pattern the blocks in this tower make? Can you make a tower using a different pattern?

DSC02111Make it ever present! Math doesn’t just have to happen at math time. Fill the classroom with tools and materials that support mathematical questioning.

  • Measure everything: Set up a measuring center and man it with rulers, tape measures, square centimeter cubes, interlocking pattern blocks, volume containers, and trundle wheels, balance scales, spring scales, step-on-scales, and gram masses, metric cylinders, measuring cups, and measuring spoons. If the tools are handy then it’s easy to say: Which is heavier? Which is longer? Which is further away?
  • Tracking time: Fill your room with clocks, stop watches and timers of all designs. And then constantly ask when children set out to do a task: How long do you think it will take? In my room I always had a timer table where children could just observe the different ways to mark time, make their own “clocks” using dripping water or grains of rice, and where they could get a child-friendly stop watch to time how fast their cars rolled or their crickets hid.
  • Calculate it: Set out calculators, cash registers, old fashioned adding machines with print out tape, abacuses, and more. And challenge them to find the sum or product, subtrahend or dividend.
  • Fill the shelves and counters with fascinating objects that invite touching, sorting and counting: Fill clear plastic bottles with buttons, bottle caps, beads, glass jewels, pebbles, sea shells, centimeter cubes, plastic bread ties, spools, screws, etc. Provide laminated Venn diagrams and graphing grids and explore, one bottle at a time.

Make it a group effort: Instead of competition to get the right answer, work together to figure out how many different ways you can find the answer or pool resources to solve problems together.

  • Be statisticians: Collect statistics about each other, projects, school happenings, and more, and create class graphs that make numbers and comparisons visual.
  • Come to agreement: If individuals get different answers, have them put their heads together and compare their methodologies. Work together until everyone agrees.

NOTE: There are many other myths about math. Here is a list of 12 others to check out: http://www.uaf.edu/deved/math/help-for-math-anxiety/12-math-myths/

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Measurement Lab: Observing Beets

beet4In this observation lab students are introduced to basic measuring tools: metric ruler, metric tape measure, balance scale and gram weights. The example lesson is drawn from a second grade class who have been presented with fresh beets to observe. However, this lesson can be done at any grade level using any type of engaging object that has measurable variability within a shared unity of appearance or form, such as apples, clam shells, corncobs, feathers, hot wheel cars, keys, leaves, lemons, nuts, seeds, pumpkins, rocks, worms, and so on. The lesson objects should be close to the same size. There should be one object for each child.

PROCEDURE

OBJECTIVES: Students will review using their senses to make observations. They will practice using measuring tools and saying and recording metric units of measure. This lesson meets these standards for Grade 2.

  • CCSS.Math.Content.2.MD.A.1 Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.
  • CCSS.Math.Content.2.MD.A.4 Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.
  • CCSS.Math.Content.2.MD.D.10 Draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories. Solve simple put-together, take-apart, and compare problems1 using information presented in a bar graph.
  • 2 PS-1-1 Plan and conduct an investigation to describe and classify different kinds of materials by their observable properties. [Clarification Statement: Observations could include color, texture, hardness, and flexibility. Patterns could include the similar properties that  different materials share.]

beet9PREPARATION

At stations around the room have set up a sensory observation table with hand lenses, a weigh station with scales and gram weights, a length stations with rulers, and a circumference table with tape measures. Have one large table where the objects can be laid out to form a physical graph on graph paper.

OBSERVE

WOW: Place chosen objects in front of the children and ask them to observe using the sensory observation lab procedure – first using their eyes, then their other senses. Elicit this observation by asking questions that draw on their memories of the sensory observation lab.

ASK QUESTIONS

Ask: Which one is the biggest? How do we know? Introduce the measuring tools. Demonstrate how to use each one to get an accurate measurement.beet10

MAKE PREDICTIONS

Next ask each child to select an object and predict its size. Record their predictions.

TEST

Their task is to go to each center to observe and measure the object.

beets1RECORD RESULTS

They are to record their results on their lab sheet. [Measurement Lab Sheet] After they have observed and measured their objects, they should place them on the graph paper from biggest to smallest.

COME TO A CONCLUSION

Discuss how they decided to order them. Did they use length, width, depth, mass,  circumference or use a combination? Does it make a difference? How does using the tools help them decide where to place them? Make bar graphs using the different ways to measure.

NEW QUESTIONS

Does the type of object affect how one measures it? Try measuring other objects.

Does it make a difference what unit of measurement is used? Try standard measures or make up your own units.

STEAM IT UP: INFUSE THE ARTS

Infuse the arts by showing students examples of scientists’ journals such as Nicky the Nature Detective and Journal of Inventions: Leonardo da Vinci and having children DSC03777draw detailed illustrations of their object in their journals using regular and colored pencil.