Tapaono L.O.s

TERM 3 Wk 4 -10

AA/AM

FRACTIONS, RATIOS and PROPORTIONS

Fraction of a Number by Addition and Multiplication (Revision)

The student uses repeated halving or known multiplication and division facts to solve problems that involve finding fractions of a set or region, renaming improper fractions, and division with remainders,

e.g., 1/3 of 36, 3 x 10 = 30, 36 – 30 = 6, 6 ÷ 3 = 2, 10 + 2 = 12

e.g., 16/3 = 5 1/3 (using 5 x 3 = 15) 3 1/3

e.g., 8 pies shared among 3 people (8 ÷ 3) by giving each person 2 pies and dividing the remaining 2 pies into thirds (answer: 2 + 1/3 + 1/3 = 2 2/3).

The student uses repeated replication to solve simple problems involving ratios and rates,

e.g. 2:3 ➝ 4:6 ➝ 8:12 etc.

AM (EARLY AP)

ADDITION and SUBTRACTION

Addition and Subtraction of Decimals and Integers

The student can choose appropriately from a broad range of mental strategies to estimate answers and solve addition and subtraction problems involving decimals, integers, and related fractions.The student can also use multiplication and division to solve addition and subtraction problems with whole numbers.

e.g., 3.2 + 1.95 = 3.2 + 2 – 0.05 = 5.2 – 0.05 = 5.15 (compensation);

e.g., 6.03 – 5.8 = □ as 6.03 – 5 – 0.8 = 1.03 – 0.8 = 0.23 (standard place value partitioning) or as 5.8 + □ = 6.03 (reversibility)

e.g., □ + 3.98 = 7.04 as 3.98 + □ = 7.04, □ = 0.02 + 3.04 = 3.06 (commutativity)

e.g., 3/4 + 5/8 = ( 3/4 + 2/8 ) + 3/8 = 1 38 (partitioning fractions)

e.g., 81 – 36 = (9 x 9) – (4 x 9) = 5 x 9 (using factors) e.g., 28 + 33 + 27 + 30 + 32 = 5 􏰀 30 (averaging) e.g., +7 – -3 = +7 + +3 = +10 (equivalent operations on integers)

PROPORTIONS AND FRACTIONS

Fractions, Ratios, and Proportions by Multiplication (Revision)

The student uses a range of multiplication and division strategies to estimate answers and solve problems with fractions, proportions, and ratios. These strategies involve linking division to fractional answers, e.g., 11÷3= 11/3 = 3 2/3

e.g., 13 ÷ 5 = (10 ÷ 5) + (3 ÷ 5) = 2 3/5

The student can also find simple equivalent fractions and rename common fractions as decimals and percentages.

e.g., 5/6 of 24 as 1/6 of 24 = 4, 5 x 4= 20 or 24 – 4 = 20

e.g., 3:5 as □ : 40, 8 x 5 = 40, 8 x 3 = 24

so □ = 24.

e.g., 3/4 = 75/100 = 75%= 0.75

ADDITION AND SUBTRACTION

Addition and Subtraction of Fractions

The student uses a range of mental partitioning strategies to estimate answers and solve problems that involve adding and subtracting fractions, including decimals. The student is 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 3/4 – 1 2/3 = 1 + (3/4 – 2/3) = 1 + (9/12 – 8/12 ) = 1 1/12

(equivalent fractions) e.g., 20 counters in ratio of 2:3 combined with 60 counters in ratio 8:7 gives a combined ratio of 1:1.

MULTIPLICATION AND DIVISION

Multiplication and Division of Decimals/ Multiplication of Fractions

The student chooses appropriately from a range of mental strategies to estimate answers and solve problems that involve the multiplication of fractions and decimals. The student can also use mental strategies to solve simple division problems with decimals. These strategies involve the partitioning of fractions and relating the parts to one, converting decimals to fractions and vice versa, and recognising the effect of number size on the answer,e.g.,3.6 x 0.75= 3/4 x 3.6 = 2.7 (conversion and commutativity);

e.g., 2/3 x 3/4 = □ as 1/3 x 1/4 = 1/12 so 2/3 of 1/4 = 2/12 so 2/3 x 3/4 = 6/12 = 1/2

e.g., 7.2 ÷ 0.4 as 7.2 ÷ 0.8 = 9 so 7.2 ÷ 0.4 = 18 (doubling and halving with place value).

PROPORTIONS AND RATIOS

Fractions, Ratios, and Proportions by Re-unitising

The student chooses appropriately from a broad range of mental strategies to estimate answers and solve problems involving fractions, proportions, and ratios. These strategies involve using common factors, re-unitising of fractions, decimals and percentages, and finding relationships between and within ratios and simple rates.

e.g., 6:9 as □ :24, 6 x 1 1/2 = 9, □ x 1 1/2 = 24, □ = 16 (between unit multiplying); or 9 x 2 2/3 = 24, 6 x 2 2/3 = 16 (within unit multiplying)

e.g., 65% of 24: 50% of 24 is 12,10% of 24 is 2.4 so 5% is 1.2, 12 + 2.4 + 1.2 = 15.6 (partitioning percentages).

Term 3 - 1 - 4 Week Plan

(Main learning focus highlighted. Highlighted blue reinforcement. Unhighlighted yet to be covered)

STRATEGY

Number:

Addition/Subtraction

Choose appropriately from a broad range of mental strategies to estimate answers and solve addition and subtraction problems involving decimals, integers, and related fractions. Use multiplication and division to solve addition and subtraction problems with whole numbers.

Multiplication/Division

Choose appropriately from a broad range of mental strategies to estimate answers and solve multiplication and division problems. These strategies involve partitioning one or more of the factors in multiplication, and applying reversibility to solve division problems, particularly those involving missing factors and remainders. The partitioning may be additive or multiplicative.

Fractions/Ratios/Proportions

Uses a range of multiplication and division strategies to estimate answers and solve problems with fractions, proportions, and ratios. These strategies involve linking division to fractional answers, e.g.,11÷3=11/3 =3 2/3

e.g., 13 ÷ 5 = (10 ÷ 5) + (3 ÷ 5) = 2 3/5

The student can also find simple equivalent fractions and rename common fractions as decimals and percentages.

Measurement:

use metric and other standard measures
make simple conversions between units, using decimals
use side or edge lengths to find the perimeters and areas of rectangles, parallelograms, and triangles and the volumes of cuboids

KNOWLEDGE

Round whole numbers and decimals with up to two places to the nearest whole number.

Know equivalent fractions and proportions for 1/2s, 1/3s, 1/4s, 1/5s, 1/10s with denominators of 10, 100, 1000, eg. 1/4 = 25/100.

Convert fractions <—> decimal <—> percentages for halves, thirds, quarters, fifths, and tenths, e.g., 3/4 = 0.75 = 75%.

Basic +/-/x/÷ facts

Order decimals up to three places, eg. 6.25 and 6.3

Know how many 10s, 100’s or 1000’s in numbers up to 1 000,000, eg. tens in 47 562