A FEW TIPS FOR ADULTS:
Allow your children to work at their own pace, and respect their “refusals“! If they close the book or skip a page, it doesn’t necessarily mean they’re giving up. They may just need a little time to think about how to solve the problems.
Ask questions rather than give answers!
If your child asks you for help, don’t give them the answer. Rather, help them focus on the problem, or their mistake, by asking targeted questions. Let your children find their own way to solve the problems, even if it’s long and convoluted. You can then help them explore other, perhaps more “clever“ ways to find solutions.
UNDERSTANDING IS THE FIRST STEP TO PROBLEM SOLVING.
Help your children work through the problems before trying to solve them. You can do this by verbalizing, drawing the steps, or using real objects. This is the easiest, yet least fun part of problem solving!
ASK, “HOW DID YOU DO THAT?“
Gradually help them get accustomed to verbalizing and explaining their thinking processes; it’s far more important for them to know how and why they came up with an answer than to know the name of the rule applied.
The situations proposed in this book are of course imaginary.
Help your children discover numbers and math in everyday life.
Get your nose out of the book and go find math!
GEOMETRIC DECORATIONS
FRORIN, ORILDE, AND GANDOLF FINALLY REACH THE MAJESTIC MINE-CITY, AND THEY WIND THEIR WAY BETWEEN THE TALL BLUE AND GREEN HOUSES. “WE LOVE MATH SO MUCH...“, SAYS THE PRINCE, “...THAT WE EVEN USE IT TO DECORATE THE SQUARES AND BUILDINGS.“
THERE ARE SOME DWARVES FINISHING A BEAUTIFULLY DECORATED SIDEWALK OUTSIDE A BUILDING. HELP THEM FINISH IT BY ATTACHING THE PAVING STONE STICKERS IN THE RIGHT ORDER, FOLLOWING THE SEQUENCE IN THE EXAMPLE. THE STICKERS ARE AT THE BACK OF THE BOOK.
BOMBUR, THE FOREMAN, SHOWS HIS ASSISTANTS THE PATTERN FOR DECORATING THE BUILDING’S FACADE. HELP THE DWARVES FINISH DECORATING THE FACADE. ATTACH THE MISSING SHAPES, USING MASTER BOMBUR’S PATTERN TO HELP YOU. YOU’LL FIND THE PIECES AMONG THE STICKERS AT THE BACK OF THE BOOK.
“LET’S EAT!“
GANDOLF, ORILDE, AND FRORIN GO AND SIT AT THE TABLE THAT’S BEEN LAID AT THE BACK OF THE ROOM. IT’S COVERED WITH AN ARRAY OF TRAYS, TANKARDS, AND FOOD. THERE ARE 7 HUNGRY GUESTS AT THE TABLE.
ORDER FORM
KIMLI, THE WAITER, NEEDS HELP TAKING THE ORDER. EVERYONE ASKS HIM QUESTIONS, AND THE CHEF EVEN ASKS HIM FOR A DRAWING. TRY ANSWERING THE QUESTIONS WITH HIM.
IN THE KITCHEN THEY WANT TO KNOW HOW MANY TIMES EACH DISH HAS BEEN ORDERED.
DISHES
DEEP-FRIED MUSHROOMS
MUSHROOM RISOTTO
MUSHROOM SOUP
MUSHROOMS WITH POLENTA
SAUTÉED MUSHROOMS
• WHICH DISH IS ORDERED THE MOST?…………………………………………………………..........
• WHICH IS ORDERED THE LEAST? ………………………………………………………………………......
• HOW MANY DINERS JUST EAT ONE DISH? ……………………………………………............
• WHICH DISH IS ORDERED THE LEAST, SAUTÉED MUSHROOMS OR MUSHROOMS WITH POLENTA?………
COLOR THE BOXES TO COMPLETE THE GRAPH. THE DISHES ARE INDICATED ON THE HORIZONTAL AXIS, AND THE NUMBER OF DWARVES WHO ORDERED THEM ARE ON THE VERTICAL AXIS.
TOWARDS THE CORE OF THE MOUNTAIN
FRORIN, ORILDE, AND GANDOLF FIND THEMSELVES ON THE SLOPE OF A MOUNTAIN. “THIS WAY!“, SAYS THE PRINCE OF THE DWARVES, AS HE REACHES A DARK WELL WITH A CAGE LIFT HANGING ON IT.
“WHAT’S THAT?“ “OUR WAY INTO THE CORE OF THE MOUNTAIN! IT’S QUITE A LONG WAY DOWN...“
“HOW BORING!“, GROANS GANDOLF. “LET’S DO SOMETHING IN THE MEANTIME!“ AND THEY IMMEDIATELY START PLAYING A LOGIC GAME!
HELP FRORIN AND ORILDE PLAY THE LOGIC GAME AGAINST GANDOLF. LOOK AT THE EQUATIONS, AND THEN FIND THE RIGHT ANSWER AMONG THE THREE OPTIONS. FIND THE STICKER AT THE BACK OF THE BOOK, AND STICK IT IN THE SPACE NEXT TO IT.
SUDDENLY, THE CAGE LIFT STARTS SHAKING OMINOUSLY. SNAP! A ROPE BREAKS AND THEY START TO FALL. “OH NOOOOO!“ GANDOLF CONCENTRATES HARD, DRAWING ON HIS MAGIC WISDOM TO CAST A SPELL TO STOP THE FREEFALL.
“TWELVE, THIRTY-SIX, TWENTY-FOUR, ARE MULTIPLES OF … AND …“
COMPLETE THE DIAGRAM TO FINISH THE SPELL.
OF ……
MULTIPLES OF ……
“THANKS, GANDOLF!“ THE TWO DWARVES BREATHE A SIGH OF RELIEF. THE MATHEMATICIAN SMILES, BUT IMMEDIATELY BECOMES SERIOUS AGAIN: “LET’S GO! THIS ADVENTURE HAS ONLY JUST BEGUN!“
“THERE’S TOO MANY FLAMES“, SHOUTS ORILDE. “GANDOLF, WHAT DO WE DO?“ “GET OUT OF HERE!“ THE MATHEMATICIAN IS GRIMMER THAN EVER. “THESE AREN’T NORMAL FLAMES. ONLY LOGIC AND KNOWLEDGE CAN KEEP THEM AT BAY.“