Fourth grade struggling with math is given an informal math assessment and parents ask: How will the informal math assessment be used to get Susie to grade level?
Susie’s informal math assessment gives us a good picture of her strengths and weaknesses. Her strengths are her ability to add or subtract four digit numbers that require renaming in all 4 place values. In addition, Susie is fluent with addition and subtraction facts. She can accurately read numbers up to 4 place values, but she is unable to accurately name any place values beyond 4 place values.
Gaps in Math Understanding
Susie’s informal math assessment revealed gaps that impact her ability to do multiplication and division. Further investigation of Susie’s inability to name place values larger than 4 digits revealed her lack of understanding that the ones, tens and hundreds are repeated in the number system as place values progress through the thousands, millions and billions. She was unable to articulate that the place to the left of the tens place was 10 ten times bigger than the tens place, and the place value to the right of the tens place value is 10 times smaller than the tens place. Writing numbers in expanded notation is one way to demonstrate an understanding of place value concepts. When asked to write numbers in expanded notation using place values, Susie was unable to connect place values to the digits in the numbers presented. Consequently, her inability to write numbers in expanded notation and her incomplete understanding of place value concepts contributes to her problem renaming place values during the multiplication process. Furthermore, Susie was unable to describe multiplication as repeated addition, so without a basic understanding of multiplication she was unable to articulate a coherent model for division which was shown by her inability to divide a double digit number by a single digit number. When Susie was asked to add fractions with like denominators, she added the numerators of each fractions and then the denominators of each of the fractions. Therefore, she does not have a basic understanding of fractions. After her informal assessment, I introduced a place value mat to her and showed her that numbers grouped together in families of ones, tens and hundreds with family names of units, thousands, millions and billions. After a few minutes of explanation and practice she was able to accurately name numbers up to 100 million with the help of the place value mat. Obviously, she will need to practice place value concepts with manipulatives, and she will need repeated exposures to master the place value concepts. Additionally, Susie is not fluent with multiplication and division facts.
Pathway to Close Gaps Identified
- Use of expanded notation to name numbers that incorporate the use of place values from ones to billions.
- Introduce the concept of multiplication as repeated addition using manipulatives.
- Introduce a graphic organizer for multiplication and division facts.
- Practice multiplication facts utilizing the graphic organizer to visualize multiplication facts.
- With the use of graphic organizers, introduce two digits, three digit and four digit numbers multiplied by a single digit number .
- With the use of graphic organizers, introduce two digit and three digit numbers multiplied by two digit numbers using a Chapter A and a Chapter B to reinforce the multiplication by ones and tens place values.
- Introduce long division using manipulatives coupled with the use of a story about sharing a treasure equally.
- With the use of graphic organizers, migrate the long division process with manipulatives to the use of an algorithm to complete the division process using pencil and paper process.
- Introduce the idea of fractions as parts of a whole and as a division problem using manipulatives and graphic representations.
- Practice making parades of equivalent fractions using graphic organizers of cakes being sequentially cut.
- Leverage the organization of a graphic organizer for multiplication facts to find the greatest common factor of the numerator and denominator of a fraction.
- Practice using the greatest common factor to simplify fractions to simplest form.
- The use of graphic organizers to model finding a parade of equivalent fractions, and using the separate parades for two different fractions to find fractions with common denominators.
- Introduce a “switch cut” of two different cakes that are originally cut into different number pieces to create two cakes with the same number of pieces.
- Introduce a “switch multiply” of two fractions with unlike denominators using an abstract, non-graphical representation to write equivalent fractions with the same denominator.