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 badgeFULL_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 symbolVALUE_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 symbolVALUE_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 symbolVALUE_PER_IMG badges per symbol = FULL_SYM * VALUE_PER_IMG badge. = FULL_SYM * VALUE_PER_IMG badges.
HALF_SYM half symbolHALF_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.