Growing a Deeper Understanding of Mathematics

Do you remember when you first learned that 4 + 6 = 10? And then you were taught that 40 + 60= 100? My mind was blown! I discovered that I could use what I learned in Kindergarten about adding to 10 to help me solve amazingly hard problems in First Grade when adding to 100. Number Sense, or the intuitive understanding of numbers is just one of the areas of mathematics that we teach and re-teach from grade to grade at Mustard Seed School. This builds connections and math fluency, and with each challenge, deeper understanding of numbers.

Ms. Spurgin and I created a comparison of how the Investigations math program accomplishes this task across many areas of mathematics. We’ve only chosen three areas, but this principle applies to each area.

In Addition, Subtraction, and the Number System, fourth graders:
• Read, write, and sequence numbers up to 10,000.
• Solving multi-digit addition problems using many strategies
• Solving multi-digit subtraction problems using at least one strategy.

And fifth graders:
• Read, write, and sequence numbers up to 100,000.
• Solve multi-digit subtraction problems using many strategies.

In Multiplication and Division, fourth graders:
• Multiplication combinations to 12X12
• Using arrays, groups, and story contexts to represent multiplication situations.
• Finding the factors of 2-digit numbers.
• Multi-digit multiplication
• 2- and 3-digit division by 1 divisor, some with remainders

And fifth graders:
• Factors of a number
• Solving 2- and 3-digit by 2-digit multiplication.
• and 2-digit divisors
• Identity property for Multiplication
• Practice using US Algorithms for multiplication and division effectively and efficiently

In Parts of a Whole, fourth graders:
• Identify fractional parts of an area.
• Identify fractional parts of a group
• Read, Write, and interpret fraction notation.
• Ordering fractions
• Read, write, and interpret decimal fractions in tenths and hundredths.

And fifth graders:
• Use fraction-percent equivalents to solve problems about the percentage of a quantity.
• Order fractions
• Add fractions through reasoning about fraction equivalents and relationships.
• Read, write, and interpret decimal fractions to 1000ths
• Order decimals to 1000ths
• Ad decimal fractions through reasoning about place value, equivalents, and representations

As you can see from the chart there is a type of “stair stepping” using what the students know about numbers, multiplying, or fractions, and building new knowledge and skills that gives them a stairway to success.