Reflection: Developing a Conceptual Understanding The Decimal Slide - Section 2: Warm up


When reteaching this lesson I felt that adding context would help students define the terms and help them talk about what each element of their "drawing" represented. This came about accidentally when some of my students did several representations really quickly and we were still waiting for some of the other groups. I asked them what real life situation their drawings or examples could represent. 

One group came up with "Jose took 50 shots from the free throw line, but only made 5 of them". This allowed me to ask questions about each diagram "what does ___ represent in terms of Jose's free throws?" The context help to tie all the diagrams and expressions together so my students could see that the 5 could be represented as a numerator, as one of ten groups of five attempts, as one section of a box that is divided into 10 sections, etc.

The real life familiar scenario also helped them make sense of and talk about equivalence as well as proportionality on a graph when that came up in the next section. When asking "if Jose were to take 600 shots from the free throw, how many would we expect him to make?" might be easier for them to talk about and model than "find 10% of 600". The meaning that is given by the context helps them attach the mathematical learning and flexibly move from one representation to another. When students come up and share their thinking or their strategy I can ask questions I can ask questions to help them make sense mathematically:

"what number would be in each section of the box model if he took 600 free throws?"

"why does it make sense that all the denominators are ten times the numerators?"

"why does it make sense that the 6 moves from the hundreds place to the tens place on the place value chart?"

"why does it make sense that Brandon multiplied the numerator and denominator by ten? what is happening when we multiply them each by ten? What is represented by the 10"

Familiar context helps my students use language they understand to talk about new mathematical ideas and helps them to address misconceptions by attaching the math to something they understand. Having students first come up with contexts on their own helps them make sense of the contexts that I provide later. 

  Developing a Conceptual Understanding: Context can help scaffold understanding
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The Decimal Slide

Unit 8: Exploring Rational Numbers
Lesson 16 of 20

Objective: SWBAT mentally calculate 10% of any number.

Big Idea: Students connect to prior knowledge of place value and fraction sense to help understand the "decimal slide".

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Math, Fractions, Number Sense and Operations, Decimals, Place Value, percent, proportional relationships, prior knowledge, Mental Math, ratios, equivalence, box diagra, rational numbers
  54 minutes
different representations
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