pre-algebra Numeracy and Arithmetic

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Multiplication algorithm with integers

Multiplication algorithm with integers

a) Multiplying decimals with a single non-zero digit. Students are told to preserve the number of decimal places (from the question to the answer). 

b) Multiplying decimals requiring the multiplication algorithm. 

Round random numbers to the closest whole number, 1, 2 or 3 decimals places.

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Divisor is double digit. There is a remainder which we express as a fraction. 

Divisor is single digit. There is a remainder which we express as a fraction. 

Issues: alignment in columns in the working - not sure what to do about it

Decimal divided by a decimal. Multiply by a power of ten to get an integer divisor. Long and short division process. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to some number of decimal places.

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Divisor is a two-digit number. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Divisor is single digit. There is a remainder which we express as a decimal by continuing the division process. Rounding is required to one decimal place. The working suggests determining the second decimal place so the student knows whether to round up or down.

Divisor is a two digit number. There is a remainder which we express as a decimal by continuing the division process. No rounding is required by design (another question will include rounding off).

Divisor is single digit. There is a remainder which we express as a decimal by continuing the division process. No rounding is required by design (another question will include rounding off).

The simplest case. Divisor is single digit. There is no remainder. 

Nice easy case except divisor is a double digit. There is no remainder. 

Natural numbers addition algorithm. 2 and 3 digit numbers. Carrying.

Decimals addition algorithm. 2 and 3 digit numbers. Carrying.

Students seem to not realise that $\frac{a}{b}\times c=c\times\frac{a}{b}=\frac{a\times c}{b}=\frac{c\times a}{b}=a\times c \div b=a\div b\times c=c\div b \times a \ne c \div (b\times a)\ldots $ etc. This question is my attempt to help rectify this.

Counting the number of significant figures and rounding integers and decimals.

Converting between giga, mega, kilo, base, milli and micro, nano. Metres, grams and litres.

Students seem to miss the fact that division is actually multiplication by the reciprocal or the inverse of multiplication. This question attempts to address that.

Subtracting a decimal with 3 decimal places from a decimal with 2 or 3 decimal places. borrowing is necessary. This was modified from a subtraction question using integers with each number divided by 1000 so the variables have names referring to ones, tens, hundreds etc.