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Scope & Sequence in American Mathematics

18 Sep

We do it all wrong!

Why?

1. To give students a wide breadth of mathematical knowledge
2. Because our teachers don’t know how to teach math very well
3. Because we don’t have our act together and repeat, repeat, and repeat
4. Because we feel the need to give TONS of the same type of problem
5. Because our students don’t GET MATH and we think that means we need more problems and more repetition

If we learn how to teach math better and don’t waste time with so many worksheets of the same problem and don’t confuse students with so many different mathematical topics, we could progress at a faster rate with knowledge retained by students.

The NCSCOS (North Carolina Standard Course of Study) has goals in 1) Arithmetic, 2) Geometry, 3) Statistics and Probability, and 4) Algebra and 5) Measurement. One day our teachers will be teaching factor trees, then the next they are switching to Geometry vocabulary (what are acute angles? What does it mean to be perpendicular?), the next day they are having the students do “pretend” Algebra, where we don’t actually do what would be done in Algebra, we hide it, with a missing addend instead of a variable, and then students are doing graphing and finding out how many combinations exist if I line up 4 books on a shelf, then they are working with the metric system and measure items using how many “book lengths.”

This breadth of knowledge is good but I fear that we lose so much by constantly shifting gears on our kids. They forget what they learned in the Geometry unit in grade 4 when they get to Grade 5 and we start all over again. The “Algebra” skills are not really helpful yet until the kids can grasp more advanced ideas and the uses of Algebra. Measurement, to some extent, is necessary – certainly telling time, using a basic ruler, and money. Probability and Statistics are very useful, but again, let’s finish one thing before we address a new thing.

Here is what I see as a draft of scope and sequence for elementary and middle school mathematics:

Grade K:
1. Skip counting – by 2’s, 3’s, 5’s, 10’s. Expanded skip counting by 5’s and 10’s. What if I start with 25 and now want to skip count by 10? Apply to learning to count money.
2. Tally counting and apply to telling time.
3. Adding – group by ability – some can add all 1 digit numbers here, some will need to just add low numbers +0, +1, +2.
4. Exchanging – Using base 10 blocks, teach the idea that for every 10 units you can trade in for a 10 block.
5. Modeling place value with 10’s blocks for units, 10’s, and 100’s.
6. Reading numbers to the 100’s.
7. Learning doubles: work on memorizing (using song is helpful) all the doubles.
8. Adding to 10 (10 + 3 = 13) Build the concept of place value.

Grade 1:
1. Mastery of counting money
2. Mastery of telling time
3. Adding numbers without regrouping
4. Using what was taught about regrouping in Kindergarten, expand to modeling addition with regrouping
5. Add place value to the 1000.
6. Teach addition strategies.
7. Introduce the concept of multiplication and how it applies to addition and begin study of multiplication
8. Begin unit on subtraction and teach subtraction strategies
9. Teach basic measurement

Grade 2
1. Review units on telling time, counting money, addition of numbers with and without regrouping, subtraction
2. Teach multiplication strategies
3. Teach concept of factors
4. Link multiplication to division
5. Begin the process of modeling with division
6. Do mixed word problems, teach wording of problems involving +, – , X
7. Expand place value
8. Introduce concept of fractions & decimals
9. Order decimal numbers
10. Do 2 digit by 1 digit multiplication

Grade 3
1. Solidify multiplication
2. Build to long division
3. Equivalent fractions
4. Adding fractions with like denominators
5. Using equivalent fractions, add with unlike denominators
6. Multiply fractions
7. Divide fractions
8. Introduce decimals and how they relate to fractions
8. Introduce concept of percent and how it relates to fractions and decimals
9. Convert between percents and decimals
10. Add and subtract with decimals
11. Discuss degrees (90, 180, 270, 360) – do turns with your body

Grade 4:
1. Introduce mixed numbers
2. Add & subtract with mixed numbers – use models
3. Convert mixed numbers to improper fractions
4. Multiply and divide with mixed numbers
5. Apply real world uses of percents (interest)
6. Discuss concept of variable
7. Use variable to represent unknown in math problems
8. Introduce Perimeter and Area and practice arithmetic by applying these two problems

Grade 5:
1. Discuss multiples and factors
2. Build factor trees
3. Find GCF and LCM (relate LCM to equivalent fractions)
4. Probabability and Statistics UNIT
5. Begin Pre-Algebra

Grade 6:
1. Algebra 1 with modifications (1/2 year)
2. Geometry Unit (1/2 year)

Grade 7:
1. Finish Algebra 1 curriculum (1/2 year)
2. Probability and Statistics UNIT (1/2 year)

Grade 8:
1. Advanced Algebra 1 (for students who are struggling – this is a full Algebra 1 class with topics from Algebra 2 introduced at a basic level) OR
2. GEOMETRY

Grade 9 – all students will be ready for Algebra 2 or Geometry

 
 

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