Maths- Week 6 Term 4 Think Board

Triangle Fractions Week 6

Word Web: Quickly

Warren Pohatu

Kowhaiwhai

What is Kowhaiwhai?

Kowhaiwhai are beautiful painted design patterns. At first, kowhaiwhai patterns can be viewed as decoration only, but closer examination shows that they involve sophisticated mathematical precision.  These patterns include symmetry, rotation, reflection and translation.

The koru or pitau is the most basic design element of kowhaiwhai. These are curving stalks with bulbs at one end. They bear a striking resemblance to the young shoot of a native fern.

After the koru or pitau, the next main motif or pattern of kowhaiwhai is the crescent or kape. This  is characterised by a line of evenly placed white circles on the outer edge of the crescent.

The koru or pitau and the kape, are all that make up the list of basic kowhaiwhai motifs. However when used in various combinations these two patterns can create many varying designs of incredible depth.

1. Why does it say that kowhaiwhai are more than just decoration?

Because in the text, it says that (At first, kowhaiwhai patterns can be viewed as decoration only, but closer examination shows that they involve sophisticated mathematical precision)

2. Describe the two main patterns of kowhaiwhai?

The Pitau/Koru and Kape

(The koru or pitau and the kape, are all that make up the list of basic kowhaiwhai motifs)

An Artform

Stories that explain the origin of kowhaiwhai all say that it is an art form secondary in importance to  wood carving (whakairo) and tattooing (ta moko). When kowhaiwhai is compared to wood-carving and tattooing, there are several contrasts.  Apart from the obvious differences of how they are created, kowhaiwhai is seen as something more temporary. It is not seen as having  lasting value, so requires no special ritual and no formal training. It is considered to be a common (noa) activity and so therefore, can be carried out by anyone.

The colours red, black and white are often the only colours that appear in kowhaiwhai patterns. Red was obtained by mixing red ochre with shark-liver oil.  Black paint was made by mixing shark oil with powdered charcoal. For white paint, taioma or pipeclay was burned then pulverised and mixed with oil.

3. Why is kowhaiwhai seen as less important than whakairo and ta moko?

(When kowhaiwhai is compared to wood-carving and tattooing, there are several contrasts.  Apart from the obvious differences of how they are created, kowhaiwhai is seen as something more temporary)

4. Do you think whakairo and ta moko was carried out by anyone?

Yes it can. Because in the text it says that (It is considered to be a common (noa) activity and so therefore, can be carried out by anyone)

Origins

One oral account from Ngati Kahungunu, traces the origin of both wood-carving and kowhaiwhai. It tells us that:

When Whiro, Haepuru and Haematua climbed up to the second heaven to obtain carvings for their house, they were told by one of the gods that the art of decorating houses with wood carvings had already been taken away by their younger brothers. Whiro and his two friends complained to the god that they could not go begging to their younger brothers for the art, so the god showed them how to embellish a house with painted designs.

Whiro and the others then descended and adorned their own house with painted designs.( Best (1982:287-8…)

5. Why couldn't Whiro, Haepuru and Haemata get carvings for their house?

6a. sophisticated

Look at these words in the article and see if you can work out their meaning from the context. Then look up and write down the definition from the dictionary

Precision- The aim or accuracy. The state or quality of being precise.

Resemblance- Forming something. The state or fact of similarity.

Motif- The next main step or subject. A recurring subject, theme, idea, etc.

Secondary-The next thing after the first. Next after the first in order, place, time.

Temporary-Something that lasts only a period of time. It lasts only for a limited period of time; not permanent.

Pulverised-I think that it is something that you lift. Reduce to fine particles.

Obtained- Capturing. Get, acquire or secure (something)

Embellished-Make something more attractive.

Adorn-make something more beautiful and attractive like decorating.

Maths- Assessment Stage 7 and 8 (2)

Addition/Subtraction Stage 7 and 8

Solve the problems below. Try to use the strategy explained in the box above each question. Make sure you show all the steps you use to solve it.

Stage 7: Advanced Multiplicative I can choose appropriately from a broad range of mental strategies to estimate answers and solve addition and subtraction problems involving decimals, integers, and fractions. I can also use multiplication and division to solve addition and subtraction problems with whole numbers.

Stage 7: Advanced Multiplicative I can split decimal numbers in parts to solve addition and subtraction problems. e.g.a)  6.03 – 5.8 = __   as 6.03 – 5 – 0.8 = 1.03 – 0.8 = 0.23 (standard place value partitioning)  or b)2.36 + 1.27 = 2 + 1 = 3,  and .3 + .2 = .5,  and .06 + .07 = .13  So 3 + .5 + .13 = 3.63

1. Shona needs a length of wood for some shelves. Her first shelf needs to be 1.27m long and the second shelf needs to be 1.86m long. How much timber does need altogether?

1.27 + 1.86=3.13

1.0 + 1.0=2.0

0.27 + 0.86=1.13

2.0 + 1.13=3.13

2. She ends up finding 2 lengths of timber that are long enough but will have to cut them to the right length. The first piece is 1.5m. How much does she need to cut off it for the first shelf?

2.0 - 1.5=0.5

2.0-1.0=1.0

2.0-0.5=1.5

1.0-1.5=0.5

Stage 7: Advanced Multiplicative I can solve addition and subtraction problems with decimal numbers by rounding and compensating. e.g.  a) 3.2 + 1.95 = (3.2 - .05) +  (1.95 + .05) = 3.15 + 2 = 5.15 Or b) 4.31 - 2.98 = 4.31 - 3 = 1.31 + .02 = 1.33

3. Dane was 1.46m tall when he last measured himself. He has since grown a further 0.47m. What is is height now?

      1.46 + 0.47=1.93

-0.03                   +0.03

 

      1.43 + 0.50=1.93

4. When Dane was 1.46m tall his little sister was  only 0.98m tall. How much taller was Dane than his sister?

         1.46 - 0.98=0.48

+0.02                      +0.02

         1.48 - 1.0=0.48

Stage 7: Advanced Multiplicative I can solve subtraction problems with decimal numbers by reversing to an addition equation then jumping up tidy numbers on a numberline (reverse and jump) e.g. 6.03 - 5.8 =  5.8 + __ = 6.03 5.8 + 0.2 = 6,  6 + 0.03 = 6.03    .2 + .03 = .23       So 6.03 - 5.8 = 0.23

5. Tiana has a container with 2.75 litres of juice in it. She uses it to fill a smaller container of juice that holds .985 litres. How much juice is left in the larger container?

2.75 - 0.985

0.985 +      = 2.75

0.985 + 0.015=1

1  + 0.75=1.75

0.015 + 0.75=0.765

1 + 0.765=1.765

Stage 7: Stage 7: Advanced Multiplicative I can solve problems involving the addition and subtraction of unlike fractions by finding common denominators and partitioning e.g. ¾  + ⅝  =  (¾  +  2/8) + ⅜ =  (¾ + ¼) + ⅜ = 1 ⅜

6. Allanah has 3/4 of a one pizza left and 5/8 of another.  How much pizza has she got altogether?

3/4 + 5/8=1 3/8

3/4 + 2/8=5/8

5/8 + 3/8=1

3/4 + 1/4=1

1 + 3/8= 1 3/8

  

Stage 7: Advanced Proportional: I can use a range of mental partitioning strategies to estimate answers and solve problems that involve adding and subtracting fractions, including decimals. I am able to combine ratios and proportions with different amounts. The strategies include using partitions of fractions and “ones”, and finding equivalent fractions.

e.g. 2 ¾ - 1 ⅔ = 2 - 1 and ¾ - ⅔ = 1 and 9/12 - 8/12 = 1 1/12  (finding equivalent fractions)

7. Tom knows that for every 20 newspapers he delivers he gets $1.60.  How many papers does he need to deliver to earn $20

20-1.6

40-3.2

60-4.8

80-6.4

100-8.0

120-9.6

140-11.2

160-12.8

180-14.4

200-16.0

220-17.6

240-19.2

250-20

8. Hannah has a cup that hold .275 litres and a container that holds 2.2 litres.  How many cupfuls does she need to fill the container.

2.2 - 0.275=1.925

0.275 +       =2.2

0.275 + 0.725=1

1 + 0.2=1.2

0.725 + 0.2=0.925

1 + 0.925= 1.925

Word Web: Auckland Museum