Deci-mats

The Ministry is migrating nzmaths content to Tāhurangi.           
Relevant and up-to-date teaching resources are being moved to Tāhūrangi (tahurangi.education.govt.nz). 
When all identified resources have been successfully moved, this website will close. We expect this to be in June 2024. 
e-ako maths, e-ako Pāngarau, and e-ako PLD 360 will continue to be available. 

For more information visit https://tahurangi.education.govt.nz/updates-to-nzmaths

Achievement Objectives
NA4-5: Know the equivalent decimal and percentage forms for everyday fractions.
Specific Learning Outcomes

Know benchmarks for converting between common fractions, decimals and percentages.

Description of Mathematics

Number Framework Stage 7

Required Resource Materials
Scissors

Deci-mats (Material Master 7-3), whole laminated copies and paper copies

Activity

Using Materials

Give the students a copy of the whole deci-mat with no divisions. Tell them that they have been given one deci-mat each. Ask them to draw a line that cuts their mat in half and to cut along the line. Tell them that you want them to fold the one-half into quarters. 

 

decimat1.

Ask them what fraction of one these new pieces will be (one-eighth). Their answers can be verified by going back to one deci-mat. Ask, “How many eighths make one half?” (four). Record this as 4/8 = 1/2. Carry out similar actions on other fractions. For example:

 decimat2.

Record this as 9/12 = 3/4. 
Ask the students to find out how many sixths are the same as two thirds. Record this as 4/6 = 3/2. Look for the students to establish relationships between the numbers in the equations and relate them back to the deci-mat model.

For example, “If you cut quarters into three equal parts you get twelfths. So three quarters will be nine-twelfths, three times as many.”
Remind the students that the decimal system only allows tenths, hundredths, thousandths, etc. to be used in renaming fractions as decimals.
Provide them with a new deci-mat and ask them to use the marks to draw on the mat lines that cut it into tenths.
After this, provide them with another deci-mat that is divided into tenths. Ask them, “If each tenth were cut into 10 equal parts how many parts would that make?” (100) “What would each part be called?” (one hundredth). Get the students to use the marks on the deci-mat to draw the hundredth partitions.

Provide the students with a copy of the deci-mat divided into thousandths and ask them how the parts were created.

Challenge them to work co-operatively to find out how many tenths, hundredths, and thousandths are equivalent to the following fractions:1/2 , 1/4 , 1/5 , 1/8 , 1/10

Record their findings in a chart to highlight the patterns:

 decimat3.

Record the equivalence of fractions as equations, e.g., 1/2 = 5/10 = 50/100 =500/1000.

Challenge the students to explain why it is not possible to divide the deci-mat into thirds using the lines. (One-third is not equivalent to an exact number of tenths, hundredths, or thousandths.)

 Using Imaging

Cut out some non-unit fractions using photocopies of the deci-mat. For example, cut out 3/5 (6 tenths). Turn the fraction piece over so that the lines are not visible. Place it on top of a laminated version of the deci-mat that is also turned over. Label the paper piece with the fraction symbol.

Challenge the students to tell you how many tenths, hundredths, and thousandths the fraction is equivalent to. Record their solutions, using both tables and equivalent fraction statements.

 decimat4.

Check the students’ ideas by turning over both the deci-mat and the fraction piece so that the lines are visible.

Provide other similar fractions for the students to image, e.g., 3/4 , 7/8 , 9/10, and 4/5. Include fractions that have simple equivalents, like 4/8 and 8/10, and fractions greater than one, like 5/4 and 8/5, so that the students generalise the concept.

For example: 8/5 would be: 

 deciamt5.

Record an equivalence statement and ask the students if they notice any pattern in the fractions. For example: 4/3 = 100/75 = 1000/750

Students should notice multiplicative relationships across the equations like, “To get 75 hundredths, you multiply both numbers by 25.” Ask them why both numbers are multiplied by the same number. Refer back to the materials if necessary with questions like, “How many parts is each quarter cut into to form hundredths?” (25).

Using Number Properties

Give the students problems that require them to rename fractions as equivalent forms or decimals. For example:

 

decimat6.

Look for the students to be able to work between and within the fractions. For example:

 

decimat7.

 

Independent Activity

Playing the game of Create Three (see Material Master 7-9) will reinforce students' knowledge of simple equivalent fractions.

Add to plan

Log in or register to create plans from your planning space that include this resource.


Level Four