Grade 2: "Split the Squirrel, Shares His Seeds"
(From: OAME)2 Lessons: 60 minutes each
Embedded Files
(From: OAME)2 Lessons: 60 minutes each
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Content
Content
Big Idea(s):
Big Idea(s):
Fractions: Sharing fractions of a set of objects
Fractions: Sharing fractions of a set of objects
Expectations:
Expectations:
Number
B2. use knowledge of numbers and operations to solve mathematical problems encountered in everyday life
B2.6 represent division of up to 12 items as the equal sharing of a quantity, and solve related problems, using various tools and drawings
B1.7 recognize that one-third and two-sixths of the same whole are equal, in fair-sharing contexts
Social-Emotional Learning (SEL) Skills in Mathematics and the Mathematical Processes
A1.Throughout this grade, in order to promote a positive identity as a math learner, to foster well-being and the ability to learn, build resilience, and thrive, students will apply, to the best of their ability, a variety of social-emotional learning skills to support their use of the mathematical processes and their learning in connection with the expectations in the other five strands of the mathematics curriculum.
In this lesson, to the best of their ability, students will learn to build relationships and communicate effectively as they apply the mathematical process of communicating (express and understand mathematical thinking, and engage in mathematical arguments using everyday language, language resources as necessary, appropriate mathematical terminology, a variety of representations, and mathematical conventions) so they can work collaboratively on math problems – expressing their thinking, listening to the thinking of others, and practising inclusivity – and in that way fostering healthy relationships.
Learning Goals
Learning Goals
We want students to understand...
We want students to understand...
how to model one third of a set of objects.
how to model one sixth of a set of objects.
that one-third and two-sixths of a set of objects are equivalent.
how to create our own drawings to show the results of fair-share problems.
Success Criteria
Success Criteria
I can...
I can...
model one third of a set of objects.
model one sixth of a set of objects.
explain why one-third and two one-sixths are equivalent to each other.
recognize and name fraction pieces.
make my own drawings to show how objects are shared fairly.
Materials
Materials
A copy of the story “Split, the Squirrel”.
A print copy of the story “Split, the Squirrel, Shares His Seeds”
A copy of the Slides for “Split, the Squirrel, Shares His Seeds”
Chart paper and markers
Students should have access to concrete materials such as colour tiles, counting chips, etc.
Exploring the Set Model of Fractions is a video that may help your students further understand equivalent fractions of a set.
Minds On: Fractions slide presentation for the number string
A copy of the number cards
A copy of the recording sheet (or a virtual example) OR a 100’s chart
Teacher Resources
Understanding unit fractions is an important step on the Fractions Learning Pathway.You can learn more about this by starting on page 12 of Paying Attention to Fractions: K-12.
Developing a strong conceptual understanding of fractions is very important. Explore Fractions Across the Curriculum to learn more about how this understanding develops.
teacher background
teacher background
Before using this lesson, read the story “Split, the Squirrel”.
Students should have had experience working with a partner.
Students should have had experience communicating their math work in writing using pictures, words and numbers. They should also have had experience orally communicating with the class during a math congress.
Students should have had experience with one-half, one-fourth and the equivalence of one-half and two one-fourths (See Grade 1 expectations B1.6 and B1.7.)
Pedagogy
Pedagogy
Minds On
Minds On
Day 1 - Minds On:
Start by having each student get eight manipulatives (eight counters, or eight colour tiles, for example.) Ask them to represent their answer with the counters as you ask the questions in this Number String.
You can use this Minds On: Fractions slide presentation (Day 1) or write these on your own board or chart paper. Even though there are pictures in the slides, students should be representing their answers using their own manipulatives. (When discussing the fraction slides, note that the colour of the magnetic tiles doesn’t coincide with the fractional units).
Number String:
How many is one-half of two?
How many is one-half of four?
How many is one-half of eight?
How many is one-fourth of eight?
How many is two one-fourths of eight?
Teacher moves: Watch to see which children know the answers, which have to figure out the answers and which may not know how to figure out the answers. After each question, ask a few students to explain their reasoning to the class. Are they counting the items in a “one for me, one for you” fashion? Do they remember what one-half means or do you need to prompt them to think about two people sharing?
Opportunity for Differentiation
Note that some teachers may need to scaffold by asking about one-fourth of four before one-fourth of eight.
Action!
Action!
Say: Remember that cute squirrel Split? We helped him count and organize his supply of nuts and seeds so he would have enough for the winter. One of the reasons Split wanted to inventory his supply was so he would be sure to have enough to share with his friends Spot, Sploush and Splash.
Say: In part one of Split’s story, Split collected 140 acorns for the winter. He also collected other seeds and nuts.
Display the picture of the Beech Nut seed and array of 8 Beech Nuts and say: To get us started today, I want you to think about how the four friends will share 8 delicious Beech Nuts that Split saved in the fall. If he shares them equally with his friends, how many will each squirrel get? (2)
Ask: What fraction of 8 would this be? What fraction of the Beech Nuts will each squirrel get? Write the answer on the board.
Say: There is more to Split’s story. (Read the story to them, until the first discussion question.) “Split, the Squirrel, Shares His Seeds”
Say: Now the squirrels will need to figure out how much each of them will get. You will be working with a partner to figure this out. Please use the chart paper to record your thinking so everyone will be able to see how you got to your answer. Make sure you tell us what fraction of the pumpkin seeds each squirrel will get and how many seeds that would be.
Give students time to work this out. (15-20+ minutes)
Opportunity for Assessment
Communication is a goal for this lesson. As you circulate during student work time, notice how students are communicating their thinking to their partner.
Opportunity for Differentiation
Different children may be ready to work with different sized numbers. Some children may only be ready for a smaller number and work with halves and fourths (multiples of 2 and 4). Others may be ready for a larger number like 42, or 66. Make sure the number you choose is a multiple of both 3 and 6.
Opportunity for Assessment
Observe students as they work.
How are they counting the seeds?
Are they counting by ones or skip counting? How do they skip count? Do they organize into groups?
Do they have one-to-one correspondence?
Do the students notice that one one-third is the same as two one-sixths?
Do they notice that the number of seeds in one-sixth is equal to half the seeds in one-third?
Teacher Moves
Throughout this lesson it is very important that you use precise language to describe the fractions. Saying “one one-third” and “two one-sixths” helps students develop an understanding of the unit fraction and how the parts relate to the whole.
Students will need access to manipulatives throughout this lesson. Either concrete or virtual manipulatives (e.g., Colour Tiles, Sets) will be effective in helping students work through the questions.
Asking “What fraction of 8 would this be?” will be a big jump in learning for grade 2 students. Refer back to the Number String from earlier if they are not sure how to figure this out. If they need to, they may use the manipulatives.
Students should have access to a variety of manipulatives they can use to help them sort the 12 “pumpkin seeds” into groups the three squirrels can share. Most of them will probably make three equal groups. Some may follow Spot’s line of thinking and make 6. (see below) If this occurs, you will have a natural segue into the discussion comparing one one-third and two one-sixths.
Consolidation Of Learning
Consolidation Of Learning
Math Congress: Gather students together again. Display at least two posters for the class to see. Discuss the strategies they used and the answers. For example, some may draw the “seeds” in an array and will be able to use this to show how they counted in groups to find the total for each squirrel. Others may use a ten-frame to organize the “seeds”. Still others may organize in loose groups that need to be counted by ones. Highlighting those groups that are organizing and counting in groups will help enforce more efficient thinking and counting.
Ask: How many seeds do you think each squirrel will get?
After the congress, continue with the story and read from the stopping point to the end.
Ask: Split says each squirrel gets one one-third, but Spot says they each get two one-sixths. Who do you think is right? Discuss this with the students.
If students do not demonstrate an understanding that one one-third of the pumpkins seeds is equal to two one-sixths of the pumpkin seeds, have them return to the manipulatives. Ask them to divide the 12 counters into six equal groups and see how many the 3 squirrels will each get. Slide 9 and 10 in the story have pictures you can use to help them see this equivalence.
Teacher Moves:
Math Congress: During a math congress, you choose two or three groups and highlight their work. Choose groups that have used efficient strategies to sort their seeds (i.e. counting in fives or tens, using a ten-frame or array to organize the seeds for more efficient counting.) Choose groups that have clearly communicated their strategy and answer on the poster (i.e. using titles and captions to label their drawing, using several different coloured markers to highlight their steps, or organizing their work to make it easier for the viewer to follow.) If you have groups that have used equivalent fractions (e.g., one one-third and two one-sixths) to describe their work definitely highlight those.
Day 2: Minds On
Day 2: Minds On
Minds On:
Start by having each child get six manipulatives (6 counters, or 6 colour tiles, for example.) Ask them to model their answer with the counters as you ask the questions in this Number String.
You can use this Minds On: Fractions Slide presentation (Day 2) or write these on your own board or chart paper. Even though there are pictures in the Slides, students should be modelling their answers using their own manipulatives. Slides for Day 2 begin on Slide #9.
How many is one-third of three?
How many is two one-thirds of three?
How many is one-sixth of six?
How many is two one-sixths of six?
How many is one-third of six?
How many is two one-thirds of six?
Opportunity for Differentiation
Instead of assigning numbers at random, you can intentionally share certain numbers to certain students - lower numbers to those having trouble with counting or with the sharing, higher numbers for those who do not struggle with this. Some students may even be ready to start thinking about some of the numbers mentally. A lower number may allow them to make this leap in understanding more quickly than a higher number.
Day 2: Action!
Day 2: Action!
Say: Yesterday we helped Split and Spot figure out how to share some pumpkin seeds. We discovered that 12 seeds could be divided into one-thirds and into one-sixths! Remember how Spot and Split didn’t agree at first, but they figured out that one one-third is equivalent to two one-sixths?
Are there other numbers we can evenly divide into one-thirds AND two one-sixths? Is 12 the only number we can do this with? Let’s test this out! I have some numbers ready for us to try. With your partner you will choose one number and then test it out. Can it be divided into one-thirds and into two one-sixths?
Have students choose a number card at random and see if it works. They should have counters available to them so they can represent this. Ask students to record their answers on paper, or by taking a picture using a classroom tablet. (Some of these will work for thirds only and some will work for thirds and sixths.)
Display the recording sheet using technology, or create one using paper. Record all information on this sheet as students discover the answers.
Students without access to physical manipulatives can use virtual manipulatives (e.g., Colour Tiles, Sets) to create collections and partition them into groups.
Opportunity for Assessment
Some students may start figuring out the thirds and sixths, especially with the lower numbers, without using any manipulatives. Encourage them to talk about this during the math congress.
Opportunity for Differentiation
Students can record their information on the recording sheet or you might consider using a 100 chart to record which answers will work and which ones will not. Circle the ones that can be shared into thirds and sixths in different colours than those that cannot.
Some students may be ready to work with numbers higher than 12.
Day 2: Consolidation
Day 2: Consolidation
When every number has been investigated, ask students if they notice any patterns in the data. (e.g. the number of counters in one-sixths is always half the number of counters in one-third.) Discuss why this is true.
Ask “How do you know that two one-sixths of an amount is equal to one one-third of the same amount?
Teacher move: Completing this chart or recording answers on a 100 chart connects to expectations C1.4 in patterning which states, Students will “create and describe patterns to illustrate relationships among whole numbers up to 100”.
Example of partially completed sheet: (TEACHER USE ONLY)
Extension
Extension
Students could work with these numbers again, figuring out how to share them with a different number of sharers (e.g. Can a number be broken into one-halves and two one-fourths?)
Ask students what to do with the “leftovers” or remainders when an amount of seeds can’t be shared evenly amongst the sharers.
Technology
Technology
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