Tile
Tactics
number concepts for decimal fractions
Describing Decimal Fractions
teacher tip
As mentioned in the previous activity, students must define the whole, or unit, when they are
working with decimal fractions. In Tile Tactics’ decimal fractions activities, the blue-covered
set of tiles represents the unit. The unit is partitioned into 100 orange tiles, called hundredthtiles (formerly known as 1-tiles). By placing yellow grouping tiles over every 10 hundredth-tiles,
students create 10 tenth-tiles (formerly known as tiles-of-10).
Note that in Tile Tactics the ten-frame representations emphasize the decimal fraction as a
fractional part of one by showing the tenth- and hundredth-tiles on the single platform that holds
the 1-tile (the unit).
It is helpful for students to use both fraction and decimal notation when first working with
decimal fractions. This activity focuses on these related notations.
Objective
The student uses ten-frame
tiles to model decimal
fractions and uses decimal
notation and fraction
notation to describe them.
Materials
• 1-tile (formerly tile-of-100)
• Activity Sheet 1: Digit and Numeral Cards
• Activity Sheet 7: Decimal/Fraction Notation
Prep
• Cut out digit cards, including the
“0.” card.
hands-on Activity
1) The student places a 1-tile on the table. As s/he removes the blue grouping tile and the yellow grouping tiles, s/he
describes the components of the 1-tile. (A 1-tile is composed of 10 tenth-tiles; the 10 tenth-tiles are composed of
100 hundredth-tiles.)
©Copyright 2015 • KP® Mathematics
New ways of learning . . . new ways of thinking
number concepts for decimal fractions
Describing Decimal Fractions (con’t)
2) The teacher removes the tiles and creates a new model of a decimal fraction to two decimal places, keeping all the
tiles on the medium ten- frame platform. (The example shows 0.38.)
3) The student and the teacher discuss how to describe the representation with numerals: just as every whole number
is described in terms of its last place (ones), every decimal, too, is described in terms of its last place.
The student . . .
• identifies the last place in the representation. (hundredths).
• skip counts the hundredths in the model starting with the tenth-tiles. (10 hundredths-20 hundredths-30
hundredths-38 hundredths).
• names the number. (38 hundredths)
• uses digit cards to describe the number of ones, tenths, and hundredths.
Note that the decimal
point separates the whole
number portion of the
number from the decimal
fraction portion of the
number. Since a full tenframe platform represents
the whole number 1, and
this ten-frame platform is
not full, the whole number
portion of the number is 0.
0.
3
8
4) The student demonstrates that the model in Step 3 is, indeed, composed of thirty-eight hundredths.
0.
©Copyright 2015 • KP® Mathematics
3
8
New ways of learning . . . new ways of thinking
number concepts for decimal fractions
Describing Decimal Fractions (con’t)
5) Using the first row of Activity Sheet 7 as an example, the student and teacher work together to complete Row 2 for
thirty-eight hundredths.
6) The teacher verbalizes several more decimal fractions for the student. The student represents the numbers,
one by one, with ten-frame tiles and completes the rows on Activity Sheet 7.
Evidence of Learning
The student uses ten-frame tiles to represent decimal fractions to two places and uses decimal notation and
fraction notation to describe them.
©Copyright 2015 • KP® Mathematics
New ways of learning . . . new ways of thinking