Finding Coins
Judy Ling
Finding Coins
Judy Ling
Belle
King
Bob
Helicopter
Fishing for goldfish And fishing for coins!
How much do they have?
Who has a greater amount?
Who has less?
King has a greater amount of money. Bob has less than King.
So many goldfish here. Let’s buy this black one. How much will that cost? How much will Belle be left with?
Helicopter is happy. Belle’s purse is empty. But there are still More coins hidden around, Waiting to be found!
their
counting
Scholastic Mathematics K Problem Solving Kit is a program comprising twenty stories aimed at consolidating students' understanding of core mathematical concepts through solving problems and developing a problem-solving mindset using age-appropriate contexts. Three problems with their accompanying solutions are woven into each story as students solve problems together with the amicable cat family. This problem solving kit can be used as part of the Scholastic Mathematics K Program, or as a standalone program to focus on developing problem solving skills and mindset.
As part of the Scholastic Mathematics K core curriculum, each Big Book is used after the corresponding chapter in the Student Book. Review A covers all the topics in Student Book A, while Review B covers those in Student Book B.
Mathematics K
PROBLEM SOLVING
TEACHER’S GUIDE
Karren Schultz-Ferrell � Duriya Aziz
Belle
King
Bob
Helicopter
Mother
Father
About Mathematics K Problem Solving
Welcome to Scholastic Mathematics K Problem Solving.
Scholastic Mathematics K Problem Solving has been developed to provide young learners opportunities to apply mathematical concepts learned to ageappropriate scenarios and tasks, for meaningful learning and to develop a problemsolving mindset. The program consolidates and enriches students’ learning and extends from the Scholastic Mathematics K core curriculum program, an innovative world-class mathematics core curriculum program focused on the development of early numeracy and problem-solving skills, based on the effective teaching and learning practices of the global top-performers in Mathematics – Singapore, Republic of Korea and Hong Kong.
The 20 Big Books and Readers and accompanying Problem Solving Teacher’s Guide cover the four strands of mathematics: Numbers and Operations, Measurement, Geometry, and Data Analysis. Each story is filled with mathematically rich illustrations that teachers can discuss with students as they follow the cat family on their adventures. The 20 Big Books and Readers are intended to be used together with the Scholastic Mathematics K core curriculum program and can also be used as an independent problem solving program with any other core curriculum program.
Problem Solving in Mathematics K
Problem solving underpins mathematics learning in Mathematics K-6 and is a tool for learning mathematics. The stories in the Problem Solving Big Books and Readers provide a context for consolidating learning and developing deep conceptual understanding. As students engage with the stories and encounter the problems the mathematics they have learned becomes meaningful and useful and they learn to apply knowledge acquired to solve the problems and develop the ability to adapt and communicate their thinking. The stories, teacher-led enquiry and accompanying learning-center-based small group, pair and independent work encourage mathematically-rich discussion and communication of mathematical ideas and thinking.
Instructional Design
Scholastic Mathematics K Problem Solving Big Books and Readers are intended to be used at the end of each chapter of the core curriculum program so that students can apply the concepts and skills they have learned to meaningful tasks, thus developing a problem-solving mindset.
Each Big Book/Reader aligns to and consolidates the learning objectives covered in the Student Book.
• Big Books / Readers 1 to 9 correspond to Chapters 1-9 in Student Book A.
• Big Books / Readers 10 to 18 correspond to Chapters 10-18 in Student Book B.
• Review A covers mathematical concepts from Big Books / Readers 1-9.
Review B covers mathematical concepts from Big Books / Readers 10-18.
Conducting the Lesson
The diagram below illustrates the instructional pathway of each problem solving lesson in the program.
Teacher arouses the students’ interest in the story through warm up activities such as question-posing, discussion of the cover and book title, and a picture walk to activate prior knowledge and personal experience, and develop connecting and predicting skills.
Interactive read aloud of the book encourages students to actively participate in meaningmaking as they solve problems encountered by the characters and then check their solutions. Students enjoy the story for its own sake while applying the mathematical knowledge acquired.
Learning center activities, which include small group, pair and independent work, provide opportunities for communication and collaboration and for the teacher to informally assess learning through evidence of mastery.
The lessons are designed for gradual release of responsibility for learning from teacher to student and icons alongside the text in the Teacher's Guide indicate the nature of the task.
Warm up (10 minutes)
A wrap-up of the lesson provides opportunities for students to reflect on their learning and to articulate it.
Icons indicate the stages of the gradual release of responsibility model of instruction.
: whole class : small group : pair : independent
The lesson starts with a 10-minute warm-up designed to engage students and pique their interest. Teachers pose questions related to the stories and have students look at the illustrations to predict the story.
The Overview provides a quick snapshot of the story and the key features and mathematical concepts and how they are incorporated in the story.
This table lists the Learning Objectives addressed in the story and its related activities.
Read and Solve (25 minutes)
As each story unfolds during the interactive read aloud, students encounter and solve three problems presented in the context of the story. The corresponding pages of the Teacher's Guide provide a systematic and user-friendly lesson plan for use with the reader, incorporating questions to ask (with suggested answers), things to point out in the illustrations as well as activities to carry out to make the story exciting and engaging, and the learning, meaningful.
Big Book/Reader pages 2-3 introduce the story, its setting and characters, and Problem 1 of the story.
Big Book/Reader page 4 provides the solution to Problem 1.
Big Book/Reader page 5 poses Problem 2.
Big Book/Reader page 6 provides the solution to Problem 2.
Big Book/Reader page 7 poses Problem 3.
Big Book/Reader page 8 provides the solution to Problem 3 and the conclusion of the story.
Consolidate and Assess (15 minutes)
Learning Center Activities after the interactive read aloud provide an opportunity for teachers to informally assess students’ understanding. They include activities for small group, pair and independent work to provide opportunities for collaboration, communication and reflection to demonstrate mastery and for the teacher to evaluate student needs for enrichment or remediation.
Wrap up (10 minutes)
Wrap up activities are designed to help students recall and Optional Activities list other opportunities for learning in the Big Book/Reader that the teacher can use for remediation or enrichment.
About the Writing Team
Karren Schultz-Ferrell is a former elementary classroom teacher with teaching experiences ranging from 2-year-olds through Grade 5. Before retiring, she was an Elementary Integrated Instructional Specialist in Montgomery County Public Schools, MD, collaboratively aligning and writing the district’s mathematics curriculum with the Common Core State Standards for Kindergarten through Grade 5. Karren is a mathematics consultant as well as co-author of Math Misconceptions, PreK-Grade 5: From Misunderstanding to Deep Understanding and Heinemann’s Math Process Standards series, Introduction to Reasoning and Proof (Grades PreK-2, Grades 3-5, and Grades 6-8).
She became involved in the PR1ME Mathematics K program writing because she loves a challenge and teaching math to young children! Karren is the author for both the PRIME Mathematics K Teachers’ Guide, and the Problem Solving Teacher’s Guide.
Judy Ling is the author of the PRIME Mathematics K Problem Solving stories. She is from New Zealand, but has lived in Singapore and Malaysia for most of her adult life. She speaks Mandarin and Bahasa Malaysia. She lives with her family in Sarawak, where she has a preschool and a tuition center. She loves working with and writing for children. Judy has a BA from Auckland University, a diploma in Mandarin from Nanyang University and a diploma in Proofreading and Book Editing from the New Zealand Institute of Business Studies.
She has been authoring books for children for nearly thirty years. She has worked with various international publishers and has written many fiction and non-fiction texts. She has also authored textbooks and workbooks for children from pre-school to secondary level.
Duriya Aziz S W PhD
Though a language specialist by training, math education found her and Dr Aziz has spent almost 20 years developing curriculum programs based on Singapore math pedagogical principles and practices for more than 20 countries, in different languages, and worked with ministries, schools and teachers on the implementation of these programs. She has written several course books, teachers resource materials, readers and published articles on pedagogy and instructional design. She has spent nearly twenty years working with educators on the implementation of the programs around the world, and observing the dynamic interplay between pedagogy and the cultural and social contexts in which they have to operate. Duriya’s focus has been on the development and implementation of programs that incorporate global best practices while remaining culturally and contextually appropriate, to drive sustainable change at a systemic level including development of teacher competence, knowledge, and independence.
Finding Coins
Overview
The cats are in their living room looking for coins. How will they help Helicopter with all the coins they find? Students help identify coins that the cats find and count sets of 1¢ coins. They arrange three amounts of money from smallest to greatest and vice versa, as well as add and subtract two quantities of cents in 1¢ denominations. Students compare two amounts of money and state which amount is greater than and less than. The Learning Center Activities further reinforce money concepts and also reinforce counting out 1¢ coins from a larger amount of 1¢ coins.
Objectives
Introduce money denominations of 1¢, 5¢, 10¢, 20¢ and 50¢
Count up to 20 cents in 1¢ coins (scattered, arrays, in 5- or 10-frames, circular) and use the vocabulary of ‘cents’ to describe the results
Count out an amount of money from a larger amount of money represented using 1¢ denominations
Compare two amounts of money between 1¢ and 10¢, and state which amount is greater than, less than or equal to the other
6
Arrange three amounts of money from smallest to greatest and vice versa 7, 8
Add or subtract two quantities of cents in 1¢ denominations (within 10¢) and represent the result with drawings or an equation to complete the number story 7, 8
Vocabulary:
coin, value, worth, cents, buy, money, amount, cost, price, greater than, less than, equal to, greater, greatest, least, smaller, smallest
Warm up
Introduce the story by posing the following questions.
• Have you ever found any coins in your home? Where did you find the coins?
• What coins did you find? Which kind of coin did you find the most of?
• What do you do with the coins you find? (E.g. give to an adult/put in a special place)
• If you save your coins, what will you buy with them?
Have students look at the book cover. Read the story title and encourage students to make a prediction about what might happen in the story.
Materials:
• Sheets of paper for recording answers as necessary
• Bags of 20 connecting cubes, 1 bag per pair
Problem 1 BB/R pp. 2–3
Give students time to notice what is happening in the cats’ living room.
Read the text to students and discuss the following questions.
Ask:
• What are the cats doing? (looking for/ counting money)
• What is Bob doing? (counting the coins in his goldfish bank) Let’s count the 1¢ coins that Bob has. How many cents does Bob have? (13¢)
• Where is King looking? (under the couch) What did he find? (a 50¢ coin) What other coin can King find at the sofa? (a 20¢ coin)
• What is Belle doing? (emptying out her bag) What's in her bag? (leftover lunch, books, house keys, wrappers, homework) Did she find any coins? (two coins) What is the value of the two coins that Belle found? (10¢ and 5¢)
• What is Helicopter doing? (E.g. He looks sad./He’s bringing a fish bowl to the living room./It looks like the fish is really sick or dead.)
Solution 1 BB/R p. 4
Have students notice how the illustration has changed. Have students look at the thought bubbles of Bob, King and Belle, and read them out. Discuss the following questions.
Ask:
• How many 1¢ coins did Bob count? Yes, there are 13¢
• King found 2 coins. Where did he find another coin? (under the cushions) What coins did he find? (50¢ coin and 20¢ coin)
• What did Belle find? (10¢ coin and 5¢ coin)
• How is Helicopter now? (E.g. He’s still sad./Bob is trying to make him feel better.)
Problem 2 BB/R p. 5
Have students describe where the cats are now. (in a park/outside by a pond)
Read the text to students and discuss the following questions.
Ask:
• What is in the pond? (goldfish and 1¢ coins)
• What do you notice about the 1¢ coins? (E.g. They are in two groups.)
• Count the 1¢ coins near Bob. (7¢) How many cents is King trying to reach? (8¢)
Have students explain how they counted the coins and discuss various strategies for counting. (E.g. We counted the longer row of Bob’s coins and that was 4¢. Then, We kept on counting the short row. 5, 6, 7. Bob has 7¢.)
Ask:
• What do you think Bob and King will do with these 1¢ coins? (Answers will vary.)
• Who found the greater amount of money in the pond? Bob or King?
• Who has less amount of money? How can you check to be sure? (E.g. count again/check with cubes)
Give pairs a bag of connecting cubes and have them use the cubes to check their answers by lining them up to compare.
Ask:
• What is Belle doing? (going to scoop out the coins with the net/trying to catch a goldfish) Why might she trying to catch a goldfish? (to give it to Helicopter because his died)
• What else is happening? Who is the cat running towards them? (E.g. Helicopter is digging a hole to bury his goldfish. /He could be the gardener. They are not supposed to be digging holes in the park or fishing in the pond.)
Solution 2 BB/R p. 6
Have students look at the thought bubbles of Bob and King.
Read the thought bubbles and discuss the following questions.
Ask:
• Did you count Bob’s 1¢ coins correctly? (Yes, he has 7¢.) How many cents did King get from the pond? (8¢)
• Why does King have the greater amount of money? (E.g. 8 is the number we count after 7, so 8 is greater. 7 is less than 8.)
• What is happening with Helicopter now? (He dug a grave for his goldfish./ He’s still sad.)
• What is the adult cat doing/saying to the kittens? (He’s the gardener and he’s scolding the cats for fishing/taking the coins out of the pond/playing in the pond.)
Problem 3
BB/R p. 7
Have students look at the illustration.
Read the text to students.
Ask: Where are Bob, Belle and King now? (at a pet shop)
Have students describe what they see at the pet shop.
Ask:
• What do you notice about the goldfish? (E.g. There are different goldfish in the tanks./There is a black and orange goldfish just like Helicopter’s goldfish that died. It’s in the tank that says 10¢.)
• Which goldfish should Bob and Belle choose for Helicopter? Why? (E.g. the one that costs 10¢ as Belle has that much money in her wallet) Can you write a number sentence if Belle buys this fish? (10¢ 10¢ = )
• If Belle buys a goldfish from the tank with 8¢ on it, would she have enough money? Use the cubes to see if Belle will have money left Can you write a number sentence for this? (10¢ 8¢ = )
Give students time to share their results. (E.g. We counted out 10 cubes. That’s how much money Belle has in her wallet. We subtracted backwards to 8. That’s how much the fish costs. We counted back two times. Belle will have 2¢ left.) Repeat this for the amount of 7¢
Ask:
• What is King doing? (E.g. King found money in the drain! He’s trying to get it out.)
• What is the value of each coin? (20¢, 10¢, 50¢)
• Which coin has the least value? (10¢ coin)
• Which coin has a greater value than the 10¢ coin? (20¢)
• Which coin has the greatest value of all three coins that King found? (50¢)
Solution 3 BB/R p. 8
Have students look at the changes in the illustration. Read the text to students and discuss the following questions.
Ask:
• Where are the cats now? (home) How are the cats feeling? (They are all happy, especially Helicopter!)
• What has made all the cats happy? (E.g. Belle bought the black and orange goldfish for Helicopter.)
• What is Helicopter doing? (feeding worms to his new goldfish)
King has a greater amount of money. Bob has less than King.
So many goldfish here. Let’s buy this black one. How much will that cost? How much will Belle be left with?
Helicopter is happy. Belle’s purse is empty. But there are still More coins hidden around, Waiting to be found!
• Does Belle have any money left? (no) How do you know? (E.g. The black and orange goldfish was 10¢. That was how much money Belle had in her wallet./Her wallet is empty on the table./The number sentence we wrote was 10¢ 10¢ = 0.)
• Did the cats use all the coins they found? (no) Explain your thinking. (E.g. Bob and King found coins that had greater values than the 1¢ coins./They didn’t use them to buy the goldfish. They will probably save them.)
• What is King thinking about? (E.g. He put the coins in order from the least to the greatest value. The 10¢ coin has the least value. The 20¢ coin is greater in value than the 10¢ coin and the 50¢ coin is worth the most!/ He's also thinking about how he can get the coins out of the drain.)
Consolidate and Assess
Learning Center Activities
Materials and Resources:
• Add and Subtract Money (TR 18.1), 1 copy per student
• 1¢ coins, 10 per student (optional)
Materials and Resources:
• Things to Buy Workmat (TR 18.2a), 1 copy per pair
• Spinner (TR 18.2b), 1 per pair
• Bags of fifteen 1¢ coins, 1 bag per pair
• Bags of connecting cubes (5 red and 5 yellow), 1 bag per pair
• Paper clip, 1 per pair
Materials and Resources:
• Counting Money (TR 18.3), 1 copy per student
Activity 1
Give each student a copy of Add and Subtract Money (TR 18.1) and explain that students are to add or subtract to solve each problem. Read the problems aloud.
Students can share their answers with a partner. Draw a number bond for each problem on the board. Select students to complete each number bond to illustrate the problem and solution.
Activity 2
Give each pair a copy of Things to Buy Workmat (TR 18.2a), Spinner (TR 18.2b), connecting cubes, a paper clip and a bag of 1¢ coins
Explain that partners take turns spinning for an item to ‘buy’.
• Each partner chooses a color of connecting cubes.
• Partner A spins and lands, for example, on the balloon. He/she locates the balloon on the workmat and states how much the balloon costs. Partner A then counts out that many 1¢ coins from the bag. Partner B checks his/her counting. Partner A places his/her color cube on the balloon on the workmat and returns the coins to the bag.
• Partner B takes his/her turn and repeats the process.
• If a player lands on an item which has a cube on it already, that player loses his/her turn. Students continue until no more items are left to ‘buy’.
Activity 3
Give each student a copy of Counting Money (TR 18.3) Students are to count the coins arranged in different ways and write the correct number.
Emphasize to students they are counting ‘cents’ and this is represented by the symbol ‘¢’.
Wrap up
10 mins
Have students share what they have learned today about money. Have them talk with a partner first before sharing with the whole class. (E.g. There are different kinds of coins. Each coin has a different value./1¢ coins are easy to count./We can order different coins from the greatest value to the least value./We buy things with money. Then, we subtract to see how much we have left.)
Optional Activities
Have students count the money the cats found on pp. 2–3 by ones. Bob found thirteen 1¢ coins (students count up to 13), King found a 50¢ coin first (students count up to 50) and then found a 20¢ coin (students count up to 20), and Belle found a 10¢ coin (students count to 10) and a 5¢ coin (students count to 5).
TR 18.1 Add and Subtract Money
Look and write.
1. Helicopter has 10¢. He buys a pencil for 9¢.
9¢
¢ – ¢ = ¢
Helicopter has ¢ left.
2. Belle has 3¢. King gives Belle 6¢. ¢ + ¢ = ¢
Belle has ¢ altogether.
5¢ ¢
10¢
7¢
