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What do a worm, a pony and an aardvark have in common? M 3 MAKING MATH MAGIC

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Making Math Magic that all students can and should learn math! that if children like math and feel successful at math -- they will learn math! there are 3 stages that children go through when learning math: –Stage 1: Using Manipulatives –Stage 2: Developing a Mental Image –Stage 3: Using Symbols We believe……

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Standards for Mathematical Practice: Make sense of problems and Make sense of problems and persevere in solving them persevere in solving them Reason abstractly and quantitatively Reason abstractly and quantitatively (contextualize and decontextualize) (contextualize and decontextualize) Construct viable arguments and Construct viable arguments and critique the reasoning of others critique the reasoning of others M3 MAKING MATH MAGIC

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Standards for Mathematical Practice: Model with mathematics Model with mathematics Use appropriate tools strategically Use appropriate tools strategically Attend to precision Attend to precision Look for and make use of structure Look for and make use of structure Look for and express regularity in Look for and express regularity in repeated reasoning repeated reasoning M3 MAKING MATH MAGIC

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To improve understanding and retention…. Students need to: Build it! Build it! Concrete Draw it! Draw it! Mental Image Write it! Write it! Symbolic SAY IT SAY IT throughout Making Math Magic

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WHY DO STUDENTS STRUGGLE WITH MEASUREMENT CONCEPTS? M 3 MAKING MATH MAGIC

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Regardless of where/how the MEASUREMENT content was moved around and edited, there are some foundational “big rocks” necessary for students to understand, retain, and be able to apply these concepts…. What are the “big rocks”? M3 MAKING MATH MAGIC

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We need to keep in mind that Measurement involves a comparison… We are comparing an attribute of an item (or situation) with a unit that has the same attribute… Length – units of length Time – units of time M3 MAKING MATH MAGIC

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Teaching Measurement… The sequence of experiences should include: Step 1 - Making Comparisons Step 2 - Using Models of Measuring Units Step 3 - Using Actual Measuring Units M3 MAKING MATH MAGIC

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Teaching Measurement… The sequence of experiences should include: 1. Making comparisons between objects by matching. 2. Comparing objects with nonstandard units. 3. Comparing objects with standard units. 4. Choosing suitable units for specific measurements. About Teaching Mathematics by Marilyn Burns M3 MAKING MATH MAGIC

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COMPARISON ACTIVITES Give each student a piece of rope or pipe cleaner (still linear, but more flexibility) and let them compare with their partner. They have to use their words to tell their comparison stories about longer, shorter, or about the same. Use a benchmark piece of rope and let students estimate if their piece is longer, shorter, or about the same. M3 MAKING MATH MAGIC

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COMPARISON ACTIVITES They are to use their benchmark unit and find: 5 Things in the room longer than my rope 5 Things in the room shorter than my rope 2 Things in the room about the same length as my rope. They can draw pictures of what they find, or write the names of the items. M3 MAKING MATH MAGIC Give each student, each set of partners, or each group of students a linear benchmark (a stick, a length of rope, a strip of tagboard, a craft stick, etc.). This same activity can be repeated later when the benchmark unit is 1-meter length of rope, or a 1-foot strip of tagboard

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Less Obvious Comparisons If students really understand length, they can compare lengths that are not always in straight lines (in preparation for Perimeter). Make some curvy or crooked paths on the floor or on the playground (chalk/masking tape). Ask students to estimate: Which path do you think is longer/shorter? Why? How can we check? M3 MAKING MATH MAGIC

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Let’s Start Measuring… M3 MAKING MATH MAGIC

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Teaching Measurement… The sequence of experiences should include: Step 1 - Making Comparisons Step 2 - Using Models of Measuring Units Step 3 - Using Actual Measuring Units M3 MAKING MATH MAGIC

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We all know to begin with non-standard units of measure, but where do we begin with non- standard units? -Let the students choose from several non-standard items (paper clips, erasers, a Cuisenaire rod, plastic straws, craft sticks, etc.) to use for measuring purposes. -Tell a story…give their measuring activity purpose. The Pet Store called and they want to build a new pen for some of their animals. They want the new pens to be longer than our desks so the animals can stretch out when they go to sleep. We need to tell them how long our desks are so they will know where to start, but this is all we have to work with. How can you use your unit to describe how long your desk is? M3 MAKING MATH MAGIC

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Why might some of the results using the same units be different? What are some common errors and misconceptions with measuring length in non- standard units? As each group finishes measuring with their units, record their results on the board and tell them that they need to select another unit to use to measure the desk again. AND/OR As each group finishes, they need to find another group who used the same unit of measure and compare their results.

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M3 MAKING MATH MAGIC Common Errors and Misconceptions Students don’t line up the units end-to-end (curve around) Use masking tape if necessary along the edge… They may overlap the units. Can you see your entire paper clip/worm? Is that important? They may leave gaps between the units Is it OK to leave space between your worms or do they need to touch?

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Using Non-standard Units

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Estimate and Measure in Non-Standard Units Make a list of things in the classroom to measure. Again, if necessary, put masking tape along the dimension of the object you want them to measure. Use a standard template for students to record their estimates and their measured results so they get in the habit of estimating before measuring.. M3 MAKING MATH MAGIC

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Example: What to measure…. What unit to use….

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Meaningful measurement and estimation of measurements depend on a personal familiarity with the unit of measure being used. Van de Walle, 2010 M3 MAKING MATH MAGIC

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Estimate then measure M3 MAKING MATH MAGIC

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Transitioning to Standard Units Students Need to First Build Their Measuring Devices… They Need To Own It! M3 MAKING MATH MAGIC

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Making our ruler M3 MAKING MATH MAGIC

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Using our ruler M3 MAKING MATH MAGIC

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Using our ruler

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For a more Tactile Experience M3 MAKING MATH MAGIC with “worms” with straw “worms”

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Let’s Measure ….. Your team has been given a mystery unit. Use this unit to measure the different colors of ribbon in your bag. Record your measurements. Now use your ruler that you made to measure each ribbon. Look for a relationship between your units. M3 MAKING MATH MAGIC

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Let’s Measure (cont.) ….. Now use your inch worm ruler that you made to measure each ribbon. Record your measurements. Can you organize your two sets of measurement to make them easier to compare? Look for a relationship between your units. M3 MAKING MATH MAGIC

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Teaching Measurement… The sequence of experiences should include: Step 1 - Making Comparisons Step 2 - Using Models of Measuring Units Step 3 - Using Actual Measuring Units M3 MAKING MATH MAGIC

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Transitioning to Standard Units Don’t Overwhelm With Detailed Rulers!!! Transition from Non-Standard to Minimal Increments… M3 MAKING MATH MAGIC

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Go Big Blue!!…

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Understanding Perimeter and Area These two concepts are “gatekeepers” for future Measurement. If students don’t understand perimeter and area, what will they do with surface area? volume? etc.?

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With your talking partner, discuss… Why do our students struggle so much with finding Perimeter and Area?

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Prancer and Arnie and their friends, Mason and Katie

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Mason and Katie loved to visit their grandparents who live in the country. They could explore the barn, walk in the woods, and play games with Granny and Papaw. But sometimes, they would get lonesome without their friends. They wanted a pet to play with.

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Katie asked her Granny if she could get a pet to keep in the country. Granny said that they could not afford to keep a pet that didn’t help out in some way. They couldn’t feed and take care of a pet that didn’t do something in return…

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Katie thought and thought about a pet that could help around the farm. When she went home, she got on her computer and looked for a helpful pet for sale.

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Finally, she found a pony. His name was Prancer, the Perimeter Pony, and he could measure the length of the sides of the field or the sides of the barn or the sides of the garden. Katie called her Granny to tell her the good news.

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When Katie visited her grandparents the next time, there was Prancer, the Perimeter Pony, out in the field! He pranced around the outside of the field and measured as he went.

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He measured the sides of the field, the barn, the garden, and the garage – he loved to measure the perimeter of everything! Papaw knew how much fencing to buy and Granny knew how much rope to buy because Prancer helped them measure PERIMETER. Granny and Papaw were pleased and Katie was very happy!

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x

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What if Prancer came to your school? How could he help you measure? How many steps do you think it would take Prancer to walk around field #1? How many steps do you think it would take Prancer to walk around field #2?

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Mason liked Prancer, but he felt like this pet really was Katie’s pet and not his. So, he asked Papaw if he could get his own pet. Papaw told him, “Mason, you know the rules. We can’t get any pets that don’t help out on the farm. And, we don’t need another perimeter pony.” “I know, Papaw,” Mason said. “I will try to find something else.”

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So, Mason went home, turned on his computer, and searched for a helpful pet. He looked for a long time before he found the perfect pet – Arnie, the Area Aardvark!

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Arnie wasn’t as perky as Prancer. He didn’t like to do much of anything, but he was very good at plopping down and measuring space. Every time he plopped down, he actually covered up a square unit. Mason couldn’t wait to tell his Granny and Papaw about Arnie the Area Aardvark!

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The next time Katie and Mason went to visit, there was Arnie! He plopped down all over the field, the barn floor, the garage, and the garden. Arnie could measure how many square units were on the inside of different places. Papaw knew how much fertilizer to use and how much concrete to buy and Granny knew how much paint to buy because Arnie could measure AREA for them. Granny and Papaw were pleased, and Mason was very happy!

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What if Arnie came to your school? How could he help you measure? How many times do you think it would take Arnie to plop down and cover up field #1? How many times do you think it would take Arnie to plop down and cover up field #2?

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Prancer the Perimeter Pony and Arnie the Area Aardvark became very good friends. Even though they both could measure, they measured very differently. Prancer pranced around the places Arnie covered.

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Before long, all of the neighbors wanted to borrow Prancer and Arnie to help them measure. Mason and Katie’s mom and dad even let them bring Prancer and Arnie home sometimes to help them measure around their house and yard.

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How many steps do you think it would take Prancer to walk around field #6? How many times do you think it would take Arnie to plop down and cover up field #6?

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How many steps do you think it would take Prancer to walk around the edge of the field #7? How many times do you think it would take Arnie to plop down and cover field #7?

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If we want to put a border around the edge of the bulletin board, who could help us measure that – Prancer or Arnie? If we want to put a rug down in the classroom to cover the floor, who could help us measure that – Prancer or Arnie?

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Classroom Practice: How many steps will it take for Prancer to prance around the perimeter of…. - an index card? - your binder? - your desk? - the poster on the wall?

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M3 MAKING MATH MAGIC

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Classroom Practice: How many Arnies will it take to cover… - an index card? - your binder? - your desk? - the poster on the wall?

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M3 MAKING MATH MAGIC

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Use your 5 one inch square tiles to create one field for Arnie and Prancer. * Sides must be connected, not just vertices… NOT

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Compare your field to the fields of your table partners…. Did we all get the same field? If we prance Prancer around our fields, would we all get the same perimeter?

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How many times can Arnie plop on your field? Compare your answer to your table mates…

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We all used 5 square tiles… Did we get the same perimeter with Prancer? Did we get the same area with Arnie? How can this happen?

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Continue to use 5 square tiles, but this time record your fields on the geo paper and FIND AS MANY FIELDS AS YOU CAN…

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What are we building with the 5 squares? WHY are we using 5 square tiles and not 4? Why are we going from using tiles to geo-board paper?

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How many different fields did you come up with?

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Dig Deeper… What if I have 24 feet of fencing? Will the same 24 feet, regardless of how I lay it out, yield the same pen?

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Dig Deeper… If I know that I have an AREA of 8 square units, can you draw me a shape?

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Go Big Blue!!…

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