Ways of direct modeling:

Join Result Unknown (JRU) problems can be solved by direct modeling using the Join All direct modeling strategy. The Join all strategy looks like this:

Problem: Mary had 4 pencils. Her teacher gave her 2 more pencils. How many pencils does Mary have now?

Joining all strategy:

• Put out 4 counters.
• Put out 2 more counters, and move the new counters to join the first pile
• Count all of the counters to get the solution.

Separate Result Unknown (SRU) problems can be solved by the Separate from strategy,

Problem: Kyle had 6 pencils. He gave 2 of his pencils to Mike. How many pencils does Kyle have now?

Separating from strategy:

• Put out 6 counters
• Take out 2 counters from the pile
• Count the counters left in the pile to get the solution

Join Change Unknown (JCU): problems can be solved by the Join To strategy.

Problem: Ted made 4 paper airplanes in the morning. How many more paper airplanes does he need to make to have 6 paper airplanes?

Join to strategy:

• Put out 4 counters (for the 4 paper airplanes Ted already has: oooo)
• Keep counting as you put out more counters until you get to 6 (you want to have 6 eventually so keep going until you get there oooo oo). Make sure you keep the new counters in a different pile
• Count the new counters to get the answer

Compare, difference unknown (CDU) problems can be direct modeled using a matching or compare strategy.

Problem: Kelly has 9 pencils. John has 6 pencils. How many more pencils does Kelly have than John?

Matching/comparing strategy:

• Make a pile of 9 counters and a pile of 6 counters
• Match up counters from the two piles side by side
• Count those counters that don't have a partner to find the solution.