The urge to race ahead means that you're denying students needed talk time, team time, and repetition--all good attributes of a solid learning program. Also, if you don't establish a strong foundation of skill, concept, knowledge, and vocabulary, you'll be making up for lost time later as the tasks deepen and broaden.
Hence, I'll continue to use the scope and sequence as a map, but I won't rush the students. I'll give them the time they need to solidify place value concepts, move on to operation fluency, and then learn fractions.
To begin the place value unit, as you may have noticed on my blog, we examined a place value model with depth and discussed the behavior of place value. At home students are studying this by completing a number of place value tasks online using Khan Academy. During RTI we are also reviewing these concepts using TenMarks, Khan and other activities.
Now as we move ahead, we'll complete the following activities.
- Creating a number line of objects that range in length from about 3,000 (3km) meters to .001 (1 mm) meters. Using proportional reasoning and metric conversions while making the number line.
- Looking at place value and metric models, then making some of our own to solidify the proportional reasoning related to these models.
- Studying place value and writing numbers with standard notation, partition notation, word form, base-ten numeral form (standard form), and expanded form. We will use numbers related to the number of days it takes each planet to complete a revolution of the sun (a year). Those are numbers that fit nicely with the math and science standards.
- We'll use those same solar system numbers to create number lines again.
- We'll practice our number skills with That Quiz.
- Then we'll use the solar system numbers again to look at how numbers change when we multiply by multiples of ten and the fractions 1/10 (.1), 1/100 (.01), and 1/1000 (.001). We'll use calculators to study this "behavior" of the base-10 system.
These activities will take about 10 days including the final assessment. After that we'll revisit the numbers as we solidify concept, skill, and knowledge related to the four operations. We'll also revisit order of operations at this time.
The new year will bring us to the start of the fraction unit, a unit they've already been introduced to and worked with as we learned measurement, studied factors and multiples, and learned about decimals.
As I focus on deep teaching, I know that rushing doesn't work--it takes time to teach and learn well. It also takes time to develop good teamwork, precision, and quality results.
I've read on the Internet that some are calling this "slow learning," and as I write today I know what they mean. Similar to the "slow food" movement, it's a movement toward deep, rich, "nutritious" learning rather than fast learning which often gives students a shaky start to learning math, a start that doesn't result in a love of or confidence with the disciplines. Don't you agree?