The Case of the Candy Mix-Up

“What a perfect night for trick-or-treating!” Tanya beamed. She twirled and her sparkly cat tail danced in the air.

“Yes!” Imani agreed. She looked up, causing her oversized firefighter’s hat to slide toward her eyes. “The full moon is so bright!”

Every Halloween, Caleb took his little sister, Tanya, and her best friend, Prisha, trick-or-treating for an hour. This time, he had invited his friends Imani, Jo, Hiro, and Luis to come along.

“Where should we go first?” asked Jo. He wore a sheet with holes for the eyes and mouth—a classic ghost costume.

Luis waved his wizard’s wand. “I have an idea,” he said. “What if we split up? That way we can go to every house in the neighborhood and still be back in an hour! Then we could divide the candy equally between the seven of us.”

“What a perfect night for trick-or-treating!” Tanya smiled. She spun around. Her cat tail sparkled.

“Yes!” Imani agreed. She was dressed as a firefighter. Her hat was too big. It almost covered her eyes. “The full moon is so bright!”

It was Halloween night. Every year, Caleb took Tanya trick-or-treating. Tanya was Caleb’s little sister. Tanya always invited her best friend, Prisha. Caleb’s parents let the group trick-or-treat for exactly one hour. This year, Caleb had invited his friends Imani, Jo, Hiro, and Luis to come with them. 

“Where should we go first?” asked Jo. He wore a sheet over his head. It had holes cut out for Jo’s eyes and mouth. It was a classic ghost costume.

“Works for me,” Caleb said. The others nodded. “We’ll keep track of how many pieces of candy we get. Let’s split into two pairs and one group of three.”

“I’ll go with Prisha!” Tanya volunteered. Prisha’s pumpkin costume wobbled as she and Tanya high-fived.

“I’ll count our candy,” Prisha promised.

“Luis, want to come with me?” Hiro asked. His superhero cape blew in the breeze.

“Sure!” Luis exclaimed. “Then Caleb, Imani, and Jo will be our group of three.”

“Perfect,” Caleb agreed. “Let’s get started!”

Each group headed off in a different direction.

Luis was dressed as a wizard. He waved his wand. “I have an idea!” he said. “Let’s split up. We can go to every house in the neighborhood that way. And we’ll still be back in an hour! After, we’ll divide the candy equally between the seven of us.”

“Sure!” Caleb said. “We’ll count how many pieces of candy we get. Let’s split up. We’ll need two groups with two people each. The last group will have three people.”

“I’ll go with Prisha!” Tanya said. Prisha and Tanya high-fived.

“I’ll count our candy,” Prisha promised. She was wearing a pumpkin costume.

“Luis, want to come with me?” Hiro asked. He was dressed as a superhero. His cape blew in the breeze.

“Sure!” Luis said. “Caleb, Imani, and Jo will be our group of three.”

“Perfect,” Caleb agreed. “Let’s get started!”

Each group walked in a different direction.

At the first house, Jo knocked on the door and tried to scare the person who opened it. Imani and Caleb laughed as they scooped up candy. Caleb pulled a small notebook out of the pocket of his detective costume. He tallied each piece that went into their bags.

Finally, they reached the edge of the neighborhood. Caleb looked at his watch. “Luis was right. It took us almost an hour to finish our section.”

The friends met in front of the Craft house. Their bags bulged with candy.

“We’ve got 280 pieces,” Prisha announced proudly. “Tanya and I just counted.”

“It’s 228 for us,” Hiro said. He pointed to Luis. “He kept track of them in his head. I don’t know how he does it!”

Caleb flipped open his notebook. “We have 360 pieces,” he said.

“Awesome,” Luis cheered. “That makes . . . 868 pieces of candy total!”

Caleb tapped his pencil against his chin. “So each of us would get . . . ”

“Hold on!” Luis said. “I want to try something.” He knelt on the sidewalk and grabbed a piece of sidewalk chalk.

Jo, Imani, and Caleb reached the first house. Jo knocked on the door. He tried to scare the person who opened it. Imani and Caleb laughed. Then all three of them scooped candy into their bags. Caleb was dressed as a detective. He pulled a small notebook out of his pocket. He tallied each piece of candy they took.

Finally, they reached the end of the neighborhood. Caleb looked at his watch. “Luis was right. It took us almost an hour to finish.”

The friends met in front of Caleb’s house. Their bags were full of candy.

“We’ve got 280 pieces,” Prisha said.

“We have 228,” Hiro said. He pointed to Luis. “He kept track of them in his head. I don’t know how he does it!”

Caleb opened his notebook. “We have 360 pieces,” he said.

“Awesome,” Luis said. “So we have 868 total pieces of candy!”

Caleb tapped his pencil against his chin. “So each of us would get . . .”

“Hold on!” Luis said. “I want to try something.” Luis sat on the sidewalk. He grabbed a piece of sidewalk chalk.

“I learned a new method of division,” Luis explained. “I’ve wanted to practice it. It’s called box division.”

Luis drew a rectangle on the sidewalk. He divided it into three columns. At the top of each column, he wrote the digits 8, 6, and 8. To the left, he wrote the number 7.

“You use multiplication and subtraction to find your answer,” Luis explained.

“That’s very cool,” Caleb said. He watched as Luis wrote subtraction signs and arrows in the box. Finally, Luis circled the numbers at the bottom.

“We each get 120 pieces of candy!”

They all quickly emptied their bags, making a pile of candy next to the chalk grid. Then each person picked 120 pieces to keep.

“118 . . . 119 . . . 120!” Hiro finished. He held up his full bag with a grin. “What a haul! Splitting up was a great idea, Luis.”

“I learned a new way to divide large numbers,” Luis explained. “I want to practice it. It’s called box division.”

Luis drew a rectangle on the sidewalk. He divided it into three columns.

At the top of each column, he wrote the digits 8, 6, and 8. To the left, he wrote the number 7.

“You use multiplication and subtraction to find your answer,” Luis explained.

“That’s very cool,” Caleb said. He watched Luis work. Luis wrote subtraction signs and arrows in the box. Finally, Luis circled the numbers at the bottom.

“We each get 120 pieces of candy!”

The friends poured all the candy out of their bags. They piled it next to the chalk grid. Then each person picked 120 pieces to keep.

“118, 119, 120!” Hiro finished. He held up his full bag. He smiled. “That’s so much candy! Splitting up was a great idea, Luis.”

“Hold on,” Luis cautioned. “That’s not right.” He scratched his head. Everyone had counted correctly, but 28 pieces of candy remained in the pile.

“Do you mind if I check your work?” Caleb offered.

Luis nodded and stepped back from the box. “I think I did the multiplication and subtraction right,” he said.

Caleb carefully checked Luis’s work. “Ah! You’re right, Luis, you did! There’s just one mistake. The method works, but we have to be careful about which number is the quotient!”

Luis peeked over Caleb’s shoulder. His eyes widened. “You’re right! Everyone, pick out four more pieces of candy.”

Tanya cheered as she scooped up four chocolate bars. “Math is the best!”she said.

“Hold on,” Luis said. “That’s not right.” He scratched his head. Everyone had counted correctly. But the pile still had 28 pieces of candy left.

“Can I check your work?” Caleb asked.

Luis nodded. He stepped back from the box. “I think I did the multiplication and subtraction right,” he said.

Caleb carefully checked Luis’s work. “Ah! You’re right, Luis. You did! There’s just one mistake. The method works. But we have to be careful about which number is the quotient!”

Luis looked over Caleb’s shoulder. “You’re right! Everyone, pick out four more pieces of candy.”

Tanya cheered. She chose four chocolate bars. “Math is the best!” she said.