randRangeUnique( 1, 7, 5 ) randFromArray([ ["meteorite", $._("meteorite")], ["moon", $._("moon")], ["earth", $._("earth")] ]) new Plural(function(num) { return $.ngettext("symbol", "symbols", num); }) new Plural(function(num) { return $.ngettext("badge", "badges", num); }) "<img src='" + Khan.imageBase + "badges/" + BADGE_ID + "-small.png'>" "<div style=\"background-image:url('" + Khan.imageBase + "badges/" + BADGE_ID + "-small.png'); width:20px; height:40px;\"> </div>" randFromArray([ 2, 4 ]) VALUE_PER_IMG === 1 ? [ 0, 0, 0, 0, 0 ] : [ rand(2), rand(2), rand(2), rand(2), rand(2) ]

Use the pictograph to answer the question below:

BADGE badges earned by each student
person( n + 1)FULL_IMAGE HALF_IMAGE
FULL_IMAGE = VALUE_PER_IMG BADGE badge FULL_IMAGE = VALUE_PER_IMG BADGE badges
rand( 5 ) DATA[ PERSON ] * VALUE_PER_IMG + HALF[ PERSON ] * VALUE_PER_IMG / 2

How many BADGE badges did person( PERSON + 1 ) earn?

ANSWER BADGE badges

The key at the bottom of the pictograph shows that each full symbol represents VALUE_PER_IMG badge.

The key at the bottom of the pictograph shows that each full symbol represents VALUE_PER_IMG badges.

Find person( PERSON + 1 )'s row in the table:

person( PERSON + 1 )FULL_IMAGE HALF_IMAGE

There is DATA[PERSON] full symbol and 1 half symbol.There are DATA[PERSON] full symbols and 1 half symbol. The full symbols represent VALUE_PER_IMG badge.The full symbols represent VALUE_PER_IMG badges. The half symbol must represent VALUE_PER_IMG/2 badge.The half symbol must represent VALUE_PER_IMG/2 badges.

`DATA[ PERSON ]` plural_form(SYMBOL_PL, DATA[ PERSON ] ) `\times` `VALUE_PER_IMG` badge per symbol `VALUE_PER_IMG` badges per symbol `= DATA[ PERSON ] * VALUE_PER_IMG` badge.`= DATA[ PERSON ] * VALUE_PER_IMG` badges.
`1` half symbol `\times VALUE_PER_IMG/2` badge per half symbol `= VALUE_PER_IMG / 2` badge.
`1` half symbol `\times VALUE_PER_IMG/2` badges per half symbol `= VALUE_PER_IMG / 2` badges.

person( PERSON + 1 ) earned `ANSWER` BADGE badge.

person( PERSON + 1 ) earned `ANSWER` BADGE badges.

rand( 5 ) DATA[ PERSON ] * VALUE_PER_IMG + HALF[ PERSON ] * VALUE_PER_IMG / 2 mixedFractionFromImproper( toFraction( VALUE / VALUE_PER_IMG, 0.001 )[0], toFraction( VALUE / VALUE_PER_IMG, 0.001 )[1] ) $._("%(point)s per badge", {point: plural_form(SYMBOL_PL, VALUE_PER_IMG )})

Who earned `VALUE` BADGE badge?Who earned `VALUE` BADGE badges?

person( PERSON + 1 )

- person( 1 )
- person( 2 )
- person( 3 )
- person( 4 )
- person( 5 )

The key at the bottom of the pictograph shows that each full symbol represents VALUE_PER_IMG badge.

The key at the bottom of the pictograph shows that each full symbol represents VALUE_PER_IMG badges.

How many symbols are needed to represent `VALUE` badge?

How many symbols are needed to represent `VALUE` badges?

`\dfrac{VALUE \text{ plural(BADGE_PL, VALUE )}}{VALUE_PER_IMG \text{ POINTS_PER_BADGE}} = NUM_SYMBOLS \text{ plural_form(SYMBOL_PL, VALUE / VALUE_PER_IMG )}`

Who has `NUM_SYMBOLS` symbol next to his name?Who has `NUM_SYMBOLS` symbols next to his name?

Who has `NUM_SYMBOLS` symbol next to her name?Who has `NUM_SYMBOLS` symbols next to her name?

???FULL_IMAGE HALF_IMAGE

person( PERSON + 1 ) has `NUM_SYMBOLS` symbol next to his name.person( PERSON + 1 ) has `NUM_SYMBOLS` symbols next to his name.

person( PERSON + 1 ) has `NUM_SYMBOLS` symbol next to her name.person( PERSON + 1 ) has `NUM_SYMBOLS` symbols next to her name.

person( PERSON + 1 ) earned `VALUE` BADGE badge.

person( PERSON + 1 ) earned `VALUE` BADGE badges.

rand( 5 ) rand( 5 ) DATA[ PERSON1 ] * VALUE_PER_IMG + HALF[ PERSON1 ] * VALUE_PER_IMG / 2 DATA[ PERSON2 ] * VALUE_PER_IMG + HALF[ PERSON2 ] * VALUE_PER_IMG / 2
( VAL1 - VAL2 ) / VALUE_PER_IMG mixedFractionFromImproper( toFraction( SYMBOL_DIFF, 0.001 )[0], toFraction( SYMBOL_DIFF, 0.001 )[1] )

How many more BADGE badges did person( PERSON1 + 1 ) earn than person( PERSON2 + 1 )?

VAL1 - VAL2 BADGE badges

The key at the bottom of the pictograph shows that each full symbol represents VALUE_PER_IMG badge.

The key at the bottom of the pictograph shows that each full symbol represents VALUE_PER_IMG badges.

Find person( PERSON1 + 1 )'s and person( PERSON2 + 1 )'s rows in the table:

person( PERSON1 + 1 )FULL_IMAGE HALF_IMAGE
person( PERSON2 + 1 )FULL_IMAGE HALF_IMAGE

person( PERSON1 + 1 ) has `PRETTY_SYM_DIFF` more symbol next to his name than person( PERSON2 + 1 ) does. person( PERSON1 + 1 ) has `PRETTY_SYM_DIFF` more symbols next to his name than person( PERSON2 + 1 ) does.

person( PERSON1 + 1 ) has `PRETTY_SYM_DIFF` more symbol next to her name than person( PERSON2 + 1 ) does. person( PERSON1 + 1 ) has `PRETTY_SYM_DIFF` more symbols next to her name than person( PERSON2 + 1 ) does.

`PRETTY_SYM_DIFF` plural_form(SYMBOL_PL, SYMBOL_DIFF ) `\times` `VALUE_PER_IMG` badge per symbol `VALUE_PER_IMG` badges per symbol `= VAL1 - VAL2` badge.`= VAL1 - VAL2` badges.

person( PERSON1 + 1 ) earned `VAL1 - VAL2` more BADGE badge than person( PERSON2 + 1 ).

person( PERSON1 + 1 ) earned `VAL1 - VAL2` more BADGE badges than person( PERSON2 + 1 ).

sum( DATA ) sum( HALF ) sum( DATA ) * VALUE_PER_IMG + sum( HALF ) * ( VALUE_PER_IMG / 2 )

How many BADGE badges were earned by everyone all together?

TOTAL BADGE badges

Start by counting the total number of BADGE symbols.

There are `FULL_SYM` symbols and `HALF_SYM` half symbols.

Each symbol represents `VALUE_PER_IMG` BADGE badge.Each symbol represents `VALUE_PER_IMG` BADGE badges. Each half symbol represents `VALUE_PER_IMG / 2` BADGE badge.Each half symbol represents `VALUE_PER_IMG / 2` BADGE badges.

`FULL_SYM` plural_form(SYMBOL_PL, FULL_SYM ) `\times` `VALUE_PER_IMG` badge per symbol `VALUE_PER_IMG` badges per symbol `= FULL_SYM * VALUE_PER_IMG` badge.`= FULL_SYM * VALUE_PER_IMG` badges.
`HALF_SYM` half symbol `HALF_SYM` half symbols `\times VALUE_PER_IMG/2` badge per half symbol`\times VALUE_PER_IMG/2` badges per half symbol `= HALF_SYM * VALUE_PER_IMG / 2` badge.`= HALF_SYM * VALUE_PER_IMG / 2` badges.

All together, everyone earned `TOTAL` BADGE badge.

All together, everyone earned `TOTAL` BADGE badges.