randRangeUnique( 1, 8, 5 ) randFromArray([ "meteorite", "moon", "earth" ]) "<img src='" + Khan.urlBase + "images/" + BADGE + "-small.png'>" "<div style=\"background-image:url('" + Khan.urlBase + "images/" + BADGE + "-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 plural( "badge", VALUE_PER_IMG )
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 plural( VALUE_PER_IMG, "badge" ).

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

There plural( "is", DATA[PERSON] ) plural( DATA[ PERSON ], "full symbol" ) and 1 half symbol. The full symbols represent plural( VALUE_PER_IMG, "badge" ), so the half symbol must represent plural( VALUE_PER_IMG/2, "badge" ).

DATA[ PERSON ] plural( "symbol", DATA[ PERSON ] ) \times VALUE_PER_IMG plural( "badge", VALUE_PER_IMG ) per symbol = DATA[ PERSON ] * VALUE_PER_IMG plural( "badge", DATA[ PERSON ] * VALUE_PER_IMG ).
1 half symbol \times VALUE_PER_IMG/2 plural( "badge", VALUE_PER_IMG / 2 ) per half symbol = VALUE_PER_IMG / 2 plural( "badge", VALUE_PER_IMG / 2 ).

person( PERSON + 1 ) earned ANSWER BADGE plural( "badge", ANSWER ).

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] )

Who earned VALUE BADGE plural( "badge", VALUE )?

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 plural( VALUE_PER_IMG, "badge" ).

How many symbols are needed to represent VALUE plural( "badge", VALUE )?

\dfrac{VALUE \text{ plural( "badge", VALUE )}}{VALUE_PER_IMG \text{ plural( "symbol", VALUE_PER_IMG ) per badge}} = NUM_SYMBOLS \text{ plural( "symbol", VALUE / VALUE_PER_IMG )}

Who has NUM_SYMBOLS plural( "symbol", VALUE / VALUE_PER_IMG ) next to his( PERSON + 1 ) name?
???FULL_IMAGE HALF_IMAGE  

person( PERSON + 1 ) has NUM_SYMBOLS plural( "symbol", VALUE / VALUE_PER_IMG ) next to his( PERSON + 1 ) name.

person( PERSON + 1 ) earned VALUE BADGE plural( "badge", VALUE ).

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 plural( VALUE_PER_IMG, "badge" ).

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 plural( "symbol", SYMBOL_DIFF ) next to his( PERSON1 + 1 ) name than person( PERSON2 + 1 ) does.

PRETTY_SYM_DIFF plural( "symbol", SYMBOL_DIFF ) \times VALUE_PER_IMG plural( "badge", VALUE_PER_IMG ) per symbol = VAL1 - VAL2 plural( "badge", VAL1 - VAL2 ).

person( PERSON1 + 1 ) earned VAL1 - VAL2 more BADGE plural( "badge", VAL1 - VAL2 ) 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 plural( "badge", VALUE_PER_IMG ) and each half symbol represents VALUE_PER_IMG / 2 BADGE plural( "badge", VALUE_PER_IMG / 2 ).

FULL_SYM plural( "symbol", FULL_SYM ) \times VALUE_PER_IMG plural( "badge", VALUE_PER_IMG ) per symbol = FULL_SYM * VALUE_PER_IMG plural( "badge", FULL_SYM * VALUE_PER_IMG ).
HALF_SYM half plural( "symbol", HALF_SYM ) \times VALUE_PER_IMG/2 plural( "badge", VALUE_PER_IMG / 2 ) per half symbol = HALF_SYM * VALUE_PER_IMG / 2 plural( "badge", HALF_SYM * VALUE_PER_IMG / 2 ).

All together, everyone earned TOTAL BADGE plural( "badge", TOTAL ).