Decimal Fraction Models Visual models for tenths, hundredths and - PDF document

Decimal Fraction Models Visual models for tenths, hundredths and thousandths may be used for investigations of decimal fraction notation, equivalent fractions, or decimal fraction multiplication. Suggested Uses  Write decimal fractions on board. Have students color in fractions to match the written symbols.  Shade different fractions onto grids, duplicate for students. Have students write appropriate names and symbols, as common fractions and decimals.  Have students shade a fraction in tenths. Ask students to draw vertical lines to show hundredths, write the shaded area in both tenths and hundredths, as common fractions and as decimal fractions. This may be extended to include percent.  Use multiplication models to represent the product of decimals visually. Mark off the size of each factor on the horizontal or vertical axis, shade the rectangle marked out. Students can use the model to match the shaded area with the algorithm for multiplying ones and tenths, by checking the partial products. In the above diagram, for example, the following partial products can be identified in the shaded area: o 2.3 x 0.7 = 1.61 o 2.3 x 2 = 4.6 Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Tenths Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Name: .......................................................... Date: ................................................ Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Hundredths Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Name: .......................................................... Date: ................................................ Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Thousandths Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Name: .......................................................... Date: ................................................ Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Multiplication Grids Name: .......................................................... Date: ................................................ Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Name: .......................................................... Date: ................................................ Handout distributed at Gallery Workshop, NCTM Denver 2013, Dr P Price

Common Fractions 1 Drawing Fractions Draw halves and then quarters or fourths on these circles. Cross out any that are not even. Try drawing the first line at different angles. Draw eighths, thirds, sixths and fifths http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.

Common Fractions 2 Finding and Folding Thirds and Sixths Rectangle Finding a third is trickier than finding a half or quarter. This is a good way to find thirds of a rectangle: 3. Fold the last 1. Take a sheet of paper. 2. edge across Fold one edge and slide it until the folded part looks the same size as the remaining page . fold the paper here halfway point 5 . Open the sheet 1 1 1 4. — — — and you will see 3 3 3 that the page is fold the paper folded into thirds . Circle Or think of holding a To find a sixth of a To find a third of a steering wheel. Your circle, first draw thirds, circle, think of a clock: hands and the bottom of then draw lines to find 10, 2 & 6 o’clock the steering wheel divide divide each third in half. and connect the lines to it into thirds. the centre. Try dividing your own circles into thirds and sixths. http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.

Common Fractions 3 Fractions on a Number Line 1. fourths or quarters 0 1 2. thirds 0 1 3. fifths 0 1 4. sixths 0 1 Count the hops on these lines and write the fractions above the markers. 1. How many hops?_______ The fractional parts are _______________ 1 — 0 1 4 2. How many hops?_______ The fractional parts are _______________ 0 1 http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.

Common Fractions 4 Cross out any number lines that do not show equal hops. Write the fractions on any lines that are show equal hops. 1. 0 1 2. 0 1 3. 0 1 4. 0 1 A half is always found at the midway point regardless of the number of other markers on the number line. (Use the finger slide or count the hops) 1 — 2 1 0 1 2 3 4 5 — — — — — 6 6 6 6 6 1 0 http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.

Common Fractions 5 Cut each Fractional Piece into Two Pieces Draw lines to cut each fractional piece in two to make Equivalent fractions new fractions. example: Write the equivalent fraction that each shape now 2  shows. 4 3 6 1  3  2 6 ____ ____ 2 4 4 8 1  1  5  2 2 10 ____ ____ ____ 3 6 4 8 8 16 Write the equivalent fraction of each of these if each fractional piece was cut in two. x2 x2 3 2 —— — 6 —— — —— — = = = 8 7 4 x2 x2 Draw lines to cut each fractional piece in three Equivalent fractions pieces to make new fractions. example: Write the equivalent fraction that each shape now 2  shows. 6 3 9 1  3  3 9 ____ ____ 2 6 4 12 5  1  1  15 3 3 ____ ____ ____ 8 24 4 12 3 9 x3 6 2 —— —— 3 —— = = = 7 8 4 http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.

Common Fractions 6 Fill in the missing numbers and shade the shapes to match. 1) 0 1 3 4 8 — — — — — — — — — 8 8 8 8 8 8 8 2) Counting in fifths 2 1 — 5 8 12 — — 5 5 3) 1 — 0 1 4 4) one fifth — 0 1 Tenths: Draw or write the missing common or decimal fraction and place it on the number line. 1) 0.4 0 1 —– http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.

Common Fractions 7 Percentages: Write the missing common or decimal fraction and place it on the num- ber line. When drawing the fraction use the divisions as a guide. N.B. You will need to find the equivalent fraction first. 1) % 1 —–– —— = 100 2 0 1 2) % —–– —— = 100 0 1 Ratio 3) % : —— = —— 0 1 100 (Remember to show as recurring decimals and percent, 4) and round to the nearest hundredth) % : —— —— = 0 1 100 Operations 1) + = 3 2 = + 6 6 http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.

Common Fractions 8 Shade then add the fractions below. Remember to use 2 different colors. 1) = + =   1 1 3 2 + = + = 4 4 Add these. Add the whole numbers, then add the fractions.   1 3 3 5 2) _________________= ______________ = _________ 6 6   3 2 3 7 3) _________________ = ______________ = _______- 9 9 To add mixed numbers, add the whole numbers then add the fractions. It may be necessary to convert the fractions to the Lowest Common Denominator. Once added, change any improper fractions to mixed numbers and then simplify where possible. + = = 9 3 18 9 — — 27 3 1 2 3 — — + — — 6 — 2 3 = 5 6 12 8 = + + + 24 24 24 24 8 Add these. Remember to simplify any fractions in the answer.   2 1 2 7 1) 6 8 _________________= _____________ = ______   2 3 4 2 2) _________________= _____________ = ______ 5 4 http://www.classroomprofessor.com Licensed for unlimited photocopying by original purchaser only.