Shopping Day
Judy Ling
Shopping Day
Belle
King
Bob
Helicopter
Let’s buy some things for school. We want fourteen markers. And twelve green pens.
We have ten markers and pens.
How many more do we get?
Here are four more markers To make fourteen. A box of ten and two more Make twelve pens.
Let’s check our list.
What else should we get?
Eleven sticks of glue and Thirteen fun stamps. Did we get enough of each?
Eleven is ten and one. We’ve got that right. Ten stamps in the tray and three more. That’s thirteen for sure!
We need a box of crayons too.
A big box of eighteen. Count the rolls of sticky tape. Do we have nineteen?
Ten in the box and eight more Make eighteen crayons. I have ten rolls of tape. You have six. We need three more. But first, get Bob out of this fix!
BOOK - PROBLEM SOLVING
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.
Shopping Day
Overview
The cats are at the store buying things for school. Can you help them count and get what they need? Students help the cats figure out how many more items they should get by counting on from a set of ten ones to determine the additional items needed. They also look at the cats’ list to figure out if they had gotten the correct number of items by decomposing numbers from 10 to 19 as ten ones and some more ones.
Objectives
Compose numbers from 10 to 15 to represent them as 10 ones and some more ones using objects and drawings 2, 3, 4
Decompose numbers from 10 to 15 to represent them as 10 ones and some more ones using objects and drawings 5, 6
Compose and decompose numbers from 10 to 19 to represent them as 10 ones and some more ones using objects and drawings
Vocabulary: ones, ten ones, some more ones
Introduce the story by posing the following questions.
• Have you gone to a store to buy things? What kind of things did you buy?
• What is your favorite store to visit? What do you like about this store?
• What kind of school supplies do you think the cats might be buying for their class? (E.g. crayons, glue sticks, markers)
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.
Conduct a picture walk and have students briefly describe what they notice about each picture. Once the picture walk is done, ask students whether they would like to change their prediction and to explain their thinking.
Read and Solve 25 mins
Materials:
• Sheets of paper for recording answers as necessary
• Bags of 20 connecting cubes, 1 bag per pair
• 10-frames (TR 13.1), 1 copy per pair
• Chart paper, several sheets
Problem 1 BB/R pp. 2–3
Give pairs a bag of connecting cubes and a copy of 10-frames (TR 13.1)
Have students look at the items in the store.
Read the text to students and ask the following questions.
Ask:
• What do you see in the store? (markers, pens, erasers, glue sticks) How many markers are in the set Belle is holding? (10) How many green pens does Bob have? (10)
Let’s buy some things for school. We want fourteen markers. And twelve green pens.
Let’s buy some things for school. We want fourteen markers. And twelve green pens.
We have ten markers and pens. How many more do we get?
• How many markers do the cats need to buy? (14) How many green pens do they want? (12) Remind students that the cats want to know how many more markers and pens they need to get. Have students count out 10 cubes on one 10-frame. Then, have them count on from 10 and put more cubes in the other 10-frame until they have 14 cubes on both 10-frames.
Ask: How many more cubes did you put on the other 10-frame to make 14? (4)
Record students’ work on chart paper. Draw two 10-frames. Have students draw 10 dots in the first 10-frame and 4 more dots in the second 10-frame. Underneath, record: ones and more ones is Have students complete the number sentence. Repeat the process for the green pens.
Solution 1 BB/R p. 4
Read the text to students.
Ask: Belle has a set of 10 markers and Helicopter has 4. Are there 14 markers? Explain your thinking. (E.g. Belle has 10 markers. We counted on from 10 by 4 to get 14.)
Ask students to count the set of markers (10) and to continue to count on the extra 4 markers (11, 12, 13, 14). Have students revisit the recording on chart paper to check their counting (10 ones and 4 more ones is 14).
Say: Bob has a box of 10 green pens. Are there any more green pens? (Yes, there are 2 more.) Do you think there are 12 green pens? (Bob is holding 10 pens in his box and King is holding 2 more pens. 10, 11, 12.) Ask students to count the pens in Bob’s open box (10) and to continue counting the extra 2 pens. Have students revisit the recording on chart paper to check their counting (10 ones and 2 more ones is 12).
Problem 2 BB/R p. 5
Have students look at the other items the cats are buying. Remind students to use the cubes and 10-frames to help them count.
Read the text to students and ask the following questions.
Ask:
• What else are the cats buying? (glue sticks and stamps)
Here are four more markers To make fourteen. A box of ten and two more Make twelve pens.
• How many glue sticks are on the list? (11) How many stamps? (13)
• How can you break apart 11 into 10 ones and some more ones? Use the cubes and 10-frames to help you. Have students share their 10-frames. (10 cubes in the left 10-frame and 1 more cube in the right 10-frame)
Draw two 10-frames on chart paper. Have students draw 10 dots in the first 10-frame and 1 more dot in the second 10-frame.
are four more markers To make fourteen. A box of ten and two more Make twelve pens.
Let’s check our list. What else should we get? Eleven sticks of glue and Thirteen fun stamps. Did we get enough of each?
Here
Have students complete the following number sentence underneath the 10-frames: (glue sticks) is the same as ones (glue sticks) and more one (glue stick). Have students remove the cubes from their 10-frames. Ask them to break apart 13 into 10 ones and some more ones using their cubes and 10-frames. Draw two more 10-frames on chart paper. Have students draw 10 dots and 3 more dots in these 10-frames. Then, have them complete the following number sentence: (stamps) is the same as ones (stamps) and more ones (stamps).
Solution 2 BB/R p. 6
Read the text to students and ask the following questions.
Ask:
• King puts 10 glue sticks in a box and he has 1 glue stick beside the box. Is that the same as 11? How do you know? (E.g. Look at the first 10-frame on the chart paper. That is like King’s box of glue sticks. There are 10 dots and 1 more dot is 11.) Remind students that 11 is 10 ones and 1 more one.
• Bob is putting 10 stamps in a box and he has 3 stamps outside the box. Is that the same as 13? What do you think? (E.g. Bob has 10 stamps in his box and if we count on from 10 by 3, we stop at 13.) Remind students that 13 is 10 ones and 3 more ones.
Problem 3 BB/R p. 7
Read the text to students and ask the following questions.
Ask:
• What other things are the cats buying? (crayons and rolls of tape)
• How many crayons do the cats need? (18)
Have students count the crayons they see.
Have students use the cubes and 10-frames to show how to break apart 18 into 10 ones and some more ones. Record their work on chart paper as: 18 (crayons) is the same as 10 ones (crayons) and 8 more ones (crayons). Tell students that the cats want to buy 19 rolls of tape.
Ask: How many rolls of tape are there? (16) How do you know? (E.g. There are 10 rolls on the table and Bob has 6 rolls on his fingers. That’s so funny!) Have students count the 10 rolls on the table and then count on the number of rolls that Bob is holding (11, 12, 13, 14, 15, 16). Record their counting as: 10 ones (rolls of tape) and 6 more ones (rolls of tape) is 16 (rolls of tape).
Solution 3 BB/R p. 8
Read the text to students and ask the following questions.
Ask:
• How many crayons are in the box Helicopter is holding? (E.g. There are only 10 crayons in this box.)
• Where are the other 8 crayons? (King is holding onto them.) Have students revisit the chart paper recording for how they broke apart 18 (18 is the same as 10 ones and 8 more ones).
Ask:
• How many rolls of tape did Belle put in the box? (10) Are there 16 rolls of tape? (Yes. Bob has 6 rolls, but they are all stuck on his fingers!) Remind students that 10 ones and 6 more ones is 16.
• Will 16 rolls of tape be enough? (E.g. No, they wanted 19.) How many more rolls of tape do they need? (3) Talk with a partner about this. Give students time to share how they figured out their answer.
Ten in the box and eight more Make eighteen crayons. I have ten rolls of tape. You have six. We need three more. But first, get Bob out of this fix!
Eleven is ten and one.
We’ve got that right. Ten stamps in the tray and three more. That’s thirteen for sure!
Eleven is ten and one. We’ve got that right. Ten stamps in the tray and three more. That’s thirteen for sure!
We need a box of crayons too. A big box of eighteen. Count the rolls of sticky tape. Do we have nineteen?
Consolidate and Assess
Learning Center Activities
Materials and Resources:
• 10 Ones and Some More Ones Workmat (TR 17.1), 2 copies per student
• Connecting cubes (enough for a small group)
• String (about 40 cm), 1 string per student
• Paper bags, 1 bag per student
Activity 1
Give each student 2 copies of 10 Ones and Some More Ones Workmat (TR 17.1), a string and a paper bag. Place the connecting cubes in the middle of the table. Explain how the activity is carried out.
• Students choose a number from 11 to 19 and place that number of cubes in a bag. They then give the bag to their partners.
• Partners count the number of cubes in the bag by arranging the cubes on their workmats in the box provided. They ‘circle’ ten cubes with the piece of string and then continue to count on the number of cubes they were given, and record the results of their counting as: ones and more ones is .
• Partners check each other’s work.
• Have pairs empty their bags. Partners think of a different number of cubes to place in their bags to give to their partner to organize (by circling 10 with the string), count, record and check.
Materials and Resources:
• 1–9 Number Board (TR 17.2), 1 copy per pair
• Counters, 9 per pair
• Connecting cubes, 70 per pair
Activity 2
Give pairs a copy of 1–9 Number Board (TR 17.2), 10 connecting cubes and 9 counters
Have each student make a stick of 10 cubes. Explain the procedure.
• Partner A places one counter on one of the numbers (e.g. 4). Partner A then places 4 more cubes beside his/her stick of 10 cubes. He/she counts on the cubes beginning at 10 (sticks of cubes): 10, 11, 12, 13, 14.
• Partner B checks his/her partner’s counting.
Materials and Resources:
• 10 Ones and Some More Ones Worksheet (TR 17.3), 1 copy per student
Wrap up
• Partner B then puts one counter on another number and repeats the process. Partner A then checks Partner B’s counting.
• Partners continue to take turns until all the numbers have been covered up.
Activity 3
Give each student a copy of 10 Ones and Some More Ones Worksheet (TR 17.3) and explain the procedure.
Students are to count the number of items and complete the number sentences.
Have students share what they have learned today about 10 ones and some more ones. Ask:
• How does circling a group of 10 objects help you to count a larger number? (It helps me count quicker because I count on from 10.)
• How can you break apart 18 into a group of ones and some more ones? (E.g. I can fill up a 10-frame with cubes. Then, I can count on 8 more cubes from 10 cubes to get 18 cubes.) Record the following on chart paper: 18 is 10 ones and 8 more ones. Have students draw circles on the chart paper and draw a loop around 10 of the circles, leaving 5 circles outside the loop. Choose another number (e.g. 19) and repeat.
Optional Activities
• Revisit pp. 2–4 and have students figure out how many erasers there are. Have them model the count using cubes.
• Ahead of time, prepare a can of 10 pencils and 7 more pencils. Have students count the pencils and record the results as: 10 ones and more ones is . Change the quantity of the pencils outside the can and repeat.
ones and more ones is .
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