MIP1501
ASSIGNMENT 3 2023
UNIQUE NUMBER: 702399
DUE DATE: 11 JULY 2023
, QUESTION 1
1. Name four types of models in learning fractions and how they can be
progressively used in an intermediate phase mathematics classroom. (8)
AREA MODEL: In the area model fractions are represented as parts of an area or
region. Useful manipulatives include rectangular, or circular fraction sets, pattern
blocks, geoboards and tangrams.
Rectangular, or circular fraction sets can be used to develop the understanding that
fractions are parts of a whole, to compare fractions, to generate equivalent fractions
and to explore operations with fractions
LINEAR MODEL: In the linear model lengths are compared instead of areas (e.g., 3/4
of an inch). Either number lines are drawn and subdivided or physical materials are
compared on the basis of length. Useful manipulatives include Cuisenaire rods or
fraction strips that are easily connected to ideas about fractions on a number line.
Cuisenaire Rods are rectangular rods, each of a different color and size, that can be
used to help students develop understanding of a range of math concepts including
addition, subtraction, multiplication, length, area, volume, and fractions.
SET MODEL: In the set model the whole is understood to be a set of objects, and
subsets of the whole make up fractional parts (e.g. ½ of the class, ¼ of a set of buttons,
1/3 of a tray of muffins). Useful manipulatives include two-color counters, centimeter
cubes, or any set of objects that can be counted (e.g. a bag of marbles).
Typically red on one side and yellow on the other two color counters can be flipped to
change their color and model various fractional parts of a set.
DISCRETE MODEL: Together with one unit being divided up in parts, we need to
foster the idea of parts or fractions of a number of things. Two-thirds of the balls are
blue and one third is white.
ASSIGNMENT 3 2023
UNIQUE NUMBER: 702399
DUE DATE: 11 JULY 2023
, QUESTION 1
1. Name four types of models in learning fractions and how they can be
progressively used in an intermediate phase mathematics classroom. (8)
AREA MODEL: In the area model fractions are represented as parts of an area or
region. Useful manipulatives include rectangular, or circular fraction sets, pattern
blocks, geoboards and tangrams.
Rectangular, or circular fraction sets can be used to develop the understanding that
fractions are parts of a whole, to compare fractions, to generate equivalent fractions
and to explore operations with fractions
LINEAR MODEL: In the linear model lengths are compared instead of areas (e.g., 3/4
of an inch). Either number lines are drawn and subdivided or physical materials are
compared on the basis of length. Useful manipulatives include Cuisenaire rods or
fraction strips that are easily connected to ideas about fractions on a number line.
Cuisenaire Rods are rectangular rods, each of a different color and size, that can be
used to help students develop understanding of a range of math concepts including
addition, subtraction, multiplication, length, area, volume, and fractions.
SET MODEL: In the set model the whole is understood to be a set of objects, and
subsets of the whole make up fractional parts (e.g. ½ of the class, ¼ of a set of buttons,
1/3 of a tray of muffins). Useful manipulatives include two-color counters, centimeter
cubes, or any set of objects that can be counted (e.g. a bag of marbles).
Typically red on one side and yellow on the other two color counters can be flipped to
change their color and model various fractional parts of a set.
DISCRETE MODEL: Together with one unit being divided up in parts, we need to
foster the idea of parts or fractions of a number of things. Two-thirds of the balls are
blue and one third is white.
