Assessment Opportunities Observations: may differ • bCuatnmsutusdt ebnetsthreecsoamgneizine and describe sets? (The objects in a set be a set.) some way—must share an attribute—to • aAnrde students identifying whole objects and sets of objects as they identify name the fractions? Conversations: Select from the prompts below to help students identify fractions. • W hat do you see at the fair? • D o you see any sets of objects or people? Why could these people be considered a set? What would the whole be? • C an you think of something that makes some of the objects or people different than the others? (e.g., 4 bottles are standing and 6 have been knocked down) How could you describe those differences as a fraction? Consolidation (25 minutes) • Hang up all student work and have a gallery walk. One or two students in each group stay with their group’s work to explain what they found in the image, while the other group members ‘stray’ to see their peers’ work. Encourage students to listen and ask questions. For example, creators of the work can ask visitors what fractions they see in the same sections of the image they examined. Students can then switch roles. • Meet as a class. Discuss how students identified area and set models and the differences between the two representations. • Building Social-Emotional Learning Skills: Critical and Creative Thinking: Ask students whether they would have thought that fractions would be in places such as the picture of the fair they just analysed. Ask where else they might see fractions, such as in other pictures, other books, or in real life. Explain that learning about math can open your eyes to math that has always been there, even though you never realized it before. Math helps us make sense of our world and helps us develop new ways of looking at it. Fractions 471
12Lesson Equal Sharing with Set Models Math Number Curriculum Expectations • B1.6 use drawings to represent, solve, and compare the results of fair-share problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts • B 1.7 represent and solve fair-share problems that focus on determining and using equivalent fractions, including problems that involve halves, fourths, and eighths; thirds and sixths; and fifths and tenths Teacher Possible Learning Goals Look-Fors • Equally partitions a set of objects into fractional parts through fair-sharing Previous Experience with Concepts: experiences Students have composed and decomposed whole • Develops an understanding that the more people who share a set of objects, sets into subsets, and have named the fractional the less of the whole (a smaller number of the objects) each person gets parts they see in the set. • Investigates how the same fractional amount can be named in different ways • Equally shares whole sets among two to eight people • Explains and/or shows how their chosen strategy creates equal shares • Explains and/or shows how the various fractional parts are equally partitioned (halves to eighths) and how they relate to the whole set • Understands that the more people who share a set, the fewer parts from the set each person gets • Uses fractional language to describe the parts and the whole • Begins to understand how a fractional part can have more than one name PMraotcheesmseast:ical About the rssaPetenrrplaodertbeceplstegrienominegvtsiinst,noogcgol,o,vlrnisnengafel,necdrctetiniangsg,o,ning communicating In grade three, the main focus of fractions is on the division of whole objects and sets of objects into equal parts and the identification of the parts with fractional names. In a literature review, Bruce, Chang, Flynn, and Yearley highlight three criteria that students must consider when creating equal shares: “1) the creation of equal sized groups or parts, 2) the organization of the correct number of groups or parts, and 3) the exhaustion of the entire collection or whole” (Bruce, Chang, Flynn, & Yearley, 2013, p. 15). While area models involve creating equal-sized fractional parts, set models involve creating groups with an equal number of objects. 472 Number and Financial Literacy
Math Vocabulary: Exhausting (using up) the entire whole for area models means adjusting the wgpfeorhaiougorutrhliepttthi,hsos,ssn,e,e,stqtih,wxuaeteahlqlflfsl,uyt,tahhlsirds, size of each equal portion so every person gets a fair share. Exhausting the entire whole with set models can be more challenging, because it may not Materials: be possible to evenly distribute or further subdivide all the separate objects set of objects (e.g., within the group. As a result, there may be a limited number of ways that candies), two-sided the whole set can be shared without creating remainders. This ties in with counters, chart paper, students’ investigation of multiplication and division (see Unit 2), since markers both involve creating equal groups, unitizing, and finding factors and Time: 60 minutes multiples of numbers. About the Lesson Students will investigate how many items each person gets when equally sharing a set of objects. Minds On (15 minutes) • Show students a set of 6 objects, such as 6 candies. • Ask students why the candies can be called a set. Ask how many candies make up this set and how this could be expressed as a fraction (e.g., six sixths). Ask what one candy represents as a fraction of the whole (e.g., one sixth). • Ask students how they could equally share this set of 6 candies between 2 friends. Students can turn and talk to a partner. • Discuss the strategies they used to share the set. (e.g., Deal them out one at a time until all the candies are gone; mentally calculate that 3 is half of 6 and give 3 candies to each person.) Ask what fractional part each person gets (e.g., one half or three sixths). Ask how they represent the same amount. • Put out 3 more candies for a total of 9 candies. Ask students whether they could share 9 candies between 2 people and why they think so. Discuss what the problem is. (e.g., There is one candy left over, so it isn’t a fair share.) Ask how they might handle this problem in real life. (e.g., Give the extra candy to another friend.) • Ask students whether they can equally share the set of 9 candies with 3, 4, or 5 friends. Students can work in pairs using counters. • Discuss students’ answers and reasoning. Working On It (20 minutes) • Students work in pairs or groups of three. Give each group 12 two-sided counters to represent candies, two markers, and a piece of chart paper. • Pose the following scenarios: Can you fairly share 12 candies among: – 2 friends? Fractions 473
– 3 friends? – 4 friends? – 5 friends? – 6 friends? – 8 friends? • Students record their findings by making drawings of their representations and naming the fractional parts that each person receives. Differentiation • For some students, you may decide to limit the number of friends that might be sharing or the number of scenarios they solve. • Students who need more of a challenge and have finished the initial scenarios can figure out whether they can fairly share 13 candies with the same numbers of friends as in the original scenarios. Assessment Opportunities Observations: • Lthisattesnomfoer the fractional language that students use and whether they see fractions, such as one half and six twelfths, are equal. • Ppraeydaictttetnhteiornesutolt whether students use their findings for one scenario to of another scenario (a different number of friends). Conversations: If students are having difficulty with fractional language, pose some of the following prompts: – W hat is the whole? How many candies are in the whole? What fraction can we use to describe that? (twelfths) – H ow many candies is each person getting? (e.g., 6) How can you use the part and the whole to name the fraction? – Look at your counters divided into two groups. What other fraction can you see? (e.g., One half is in one group and one half is in the other group.) – C an six twelfths and one half mean the same thing? Why? Show it with your counters. 474 Consolidation (25 minutes) • Have student groups meet with another group to discuss how they equally shared the set of candies. Groups check each other’s work to see if the fractional names assigned are accurate. • As a class, have students share some of the strategies they used for sharing. Have students explain how they were or were not able to create equal sharing for different numbers of friends. Discuss and compare the strategies they used. (e.g., Divide in half to make halves, then divide each half again to make fourths; make 6 groups with one candy in each and keep placing one candy Number and Financial Literacy
in each until they are all gone.) Have students describe the equal shares using fractional language. Regularly ask what the whole is. • Ask whether they knew that the candies could not be equally shared among a certain number of friends before working with concrete materials. • Ask students what happens to the number of candies that each person receives as the candies are shared with more people. • Have students compare thirds to sixths (e.g., thirds have twice as many candies). Further Practice • Independent Problem Solving in Math Journals: Students can answer the following problem, using a diagram: – Twenty students are divided into five equal groups. One group goes to line up in the hall. What fraction of the students is still in class? Show your work. Fractions 475
13Lesson Equal-Sharing Problems Math Number Curriculum Expectations • B1.6 use drawings to represent, solve, and compare the results of fair-share Teacher problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 Look-Fors sharers, including problems that result in whole numbers, mixed numbers, and fractional amounts Previous Experience with Concepts: • B1.7 represent and solve fair-share problems that focus on determining and Students have solved equal-sharing problems using equivalent fractions, including problems that involve halves, fourths, involving sets. and eighths; thirds and sixths; and fifths and tenths Possible Learning Goal • Applies understanding of sets of fractions to solve a problem • Understands what the problem is asking and explains it using their own words • Selects a strategy and explains why it works • Creates equal sets of two sizes (sets of 2 and sets of 4) and explains what they represent • Counts the number of animals by realizing that a group of four legs represents a sheep and a group of two legs represents a chicken • Finds at least one solution to the problem • Names the number of sheep and chickens as fractions of the whole set of animals • Sees patterns in the solutions (e.g., the more sheep, the fewer the chickens) PMraotcheesmseast:ical About the rssaPetenrrplaodertbeceplstegrienominegvtsiinst,noogcgol,o,vlrnisnengafel,necdrctetiniangsg,o,ning communicating As students practise newly learned concepts, it is important that they can apply this knowledge to problem-solving situations. It is beneficial if they can work with open-ended problems. Marian Small describes an open-ended task as a “task that can be approached very differently, but meaningfully, by students at different developmental levels. A key feature of such a task is that there are many possible answers, and many ways to get to the answers” (Small, 2009, p. 642). Such tasks help students realize there are many real-life problems that have more than one solution. They also allow students to be creative in their thinking and help them view math as being not just about getting ‘the’ answer. Students also have opportunities to explain their thinking and look at problems from other people’s perspectives. 476 Number and Financial Literacy
MaplraletfvrhiaocVutosioclynaabinluwltahorisryd:usnuitsed About the Lesson In this lesson, students solve an open-ended task that involves equal sharing and describe their results using fractional language. In the Consolidation, the possible solutions are presented in a table so students can look for patterns and trends in the data. As students solve the problem, it is a good opportunity to reinforce the mathematical modelling process and its four components: • Understand the Problem • Analyse the Situation • Create a Model • Analyse and Assess the Model Use an anchor chart of the model to highlight how students move back and forth among the four components throughout the process. For example, if students are testing out their model and it is not working, they may have to revisit the problem (Understand the Problem), or reanalyse the conditions or context of the problem (Analyse the Situation) in order to select more appropriate strategies or tools for their model. There are some suggestions within the lesson on how and when to reinforce the model, although these will need to be adapted so they are responsive to how your students progress throughout the process. Materials: Minds On (20 minutes) concrete materials, • Pose the following problem: chart paper – There are some sheep and some chickens in the barnyard. There are 20 Time: 65 minutes legs in total. How many of each animal might there be? What fraction of all of the animals are sheep? What fraction of all of the animals are chickens? • Have students explain the problem in their own words. (Understand the Problem) • Have students turn and talk to a partner about any questions they might have about this problem without actually answering the problem. As a class, discuss their questions. (e.g., Can there be only chickens? Can there be only sheep? No; there problem says there are some of each.) (Analyse the Situation) • Ask what fraction of the animals are sheep if there is 1 sheep and 3 chickens (((e1443.goo.,ff the animals are sheep). Ask what fraction of the animals are chickens the animals are chickens). Ask what they notice about the two fractions they add up to the whole, which is 44 ). Fractions 477
Working On It (25 minutes) • Tell students they are going to solve the problem using any strategies or tools that they would like. Encourage them to find more than one solution to the problem. (Create a Model) • They can record their solutions on chart paper in any way they choose. Differentiation • You may want to reduce the number of legs in the problem for some students. • For students who need more or a challenge, tell them that there are sheep, chickens, and bees in the barnyard. Ensure that they know bees have 6 legs. Assessment Opportunities Observations: • Do students understand that there are multiple solutions? • Doroatrheetyheuyseraansdyostmemlyasteiclescttriantgegnyu(me.bg.e,rasdtdointrgy?one more sheep every time), Conversations: If students haven’t found all possibilities or if they are having difficulty seeing patterns in the possible solutions (e.g., if you add more sheep, there are fewer chickens), you may need to revisit the problem and its conditions (understand the problem/analyse the situation). Pose some of the following prompts: – How do you know you have found all of the combinations of sheep and chickens? – C ould you add another sheep? Where would the legs have to come from? (e.g., the chickens) Would you have more or fewer chickens if you added a sheep? Why? – Y ou have 3 sheep and 6 chickens. Could you add one more chicken? Why? Could you add 2 chickens? Where are the legs coming from? (the sheep) Consolidation (20 minutes) • Strategically select students’ solutions so you are sharing one of all possible answers. Discuss how students solved the problem. Record their information in a table. Number of Number of Number of Number of Number of Sheep Sheep Legs Chickens Chicken Legs Animals 1 9 2 4 8 16 8 3 8 6 12 7 4 12 4 8 6 16 2 4 478 Number and Financial Literacy
• Have students analyse the table and check for patterns. (e.g., The more sheep there are, the fewer chickens there are; there are always two more chickens when there is one less sheep.) Ask how they can see some of these patterns in the numbers. (e.g., The number of chickens goes down by two every time the number of sheep goes up by one.) • Together, review the fractions students found and how they found them. Use the chart to identify the fractional amounts (e.g., 2 out of 8 animals are sshheeeepp,awrehiicnhcliusd28edo.r(e14.)g..,ATshkewyhkaeteips happening to the fractions as more getting larger.) Compare these fractions to the benchmark of one half so students have an idea how they compare. • Ask students whether the 20 legs could be made up of all sheep or all chickens and to explain why they think so. • Ask students why they think their strategies and tools were helpful in solving the problem. Ask if there is something they would do differently if they were to solve a similar problem. (Analyse and Assess the Model) • B uilding Social-Emotional Learning Skills: Critical and Creative Thinking: Ask students how they felt while solving this problem. Ask how using their imaginations helped them find different ways to solve the problem. Discuss how hearing another person’s idea helped them think of more ideas. Emphasize that creativity and sharing ideas play important roles in the work of a mathematician. Materials: Math Talk: concrete materials Math Focus: Applying unitizing to find fractional parts of a set when the such as counters number of equal groups and the number of items in each group are known About the As previously explained, unitizing involves simultaneously seeing a group of objects as one unit (one group) and also more than one unit (the number of items in the group). This skill takes a great deal of time and experience to fully develop. It also plays an important role in helping students understand equivalent fractions. In this Math Talk, students define fractional amounts by either seeing the group as one unit or seeing each object in the group as one unit. They discover that the different fractions from the two scenarios are equal. Let’s Talk Select the prompts that best meet the needs of your students. • We have been investigating fractions by making equal shares with sets. What do we need to remember when we are equally sharing? (e.g., All people in a group get the same number of objects and there cannot be any objects left over.) continued on next page Fractions 479
Teaching Tip • Listen to this problem: There are 4 packages of pencils with 5 pencils in each Integrate the math package. What fraction of the total amount of pencils does one package talk moves (see represent? Turn and talk to your partner. You can use concrete materials to page 8) throughout solve the problem. Math Talks to maximize student • Let’s talk about what you know about the problem first. (e.g., We know there participation and active listening. are 4 packages and 5 pencils in each.) Do these represent the parts or the whole of the amount? What do you need to know before you can figure out any fraction? (e.g., the whole) How many pencils are there altogether? (e.g., We made 4 piles with 5 counters in each and counted 20 counters, so it would be 20 pencils.) What fractional amount of the whole do the 5 pencils represent? (e.g., 250 ) • Let’s look at the problem another way. What would be the whole if we are only looking at the number of packages? (e.g., 4 packages) What part would one package represent of the whole? (e.g., 41 ) • So, we have named the same group in two ways, as five twentieths and as one fourth. How can you prove that these fractions represent the same? Let’s look at our piles of counters. Can you visualize one fourth and five twentieths at the same time? Do they represent the same thing? (e.g., Yes, because they both represent the same number of pencils whether we are looking at the packages as the whole or the number of pencils as the whole.) Materials: Math Talk: chart paper Math Focus: Equally partitioning a number line About the When solving problems and communicating ideas, number lines are one of the most powerful mathematical thinking tools. “They are particularly effective for helping students understand everything about fractions including equal partitions, comparing fractions, identifying equivalent fractions and operations with fractions” (Ontario Ministry of Education, 2018, p. 4). Unlike area models, which are two-dimensional, and volume models, which are three-dimensional, number lines are one-dimensional with length/distance as the attribute being considered. Students can learn how to partition a number line into equal fractional parts. They discover that it is important to pay attention to the endpoints and to think proportionately about how they affect the names of the fractional parts. The length of the number line also affects the placement of the fractional values. Extending the number line past one whole is also an important visual to help students understand that fractions can represent more than one whole. 480 Number and Financial Literacy
Let’s Talk Select the prompts that best meet the needs of your students. • We are going to investigate how to represent fractions on a number line. What do you already know about number lines? Show an open number line, with endpoints 0 and 100, drawn on a long strip of chart paper. Where would you put 50 on this number line? Why? What other values could you put on, knowing where 50 is? (e.g., 25, 75, 40, 60) Mark some of these values on the number line. How do you know that these values are in a reasonable place on the number line? • Show students the following number line drawn on a long strip of chart paper, ensuring it is the same length as the previous number line. 01 • W hat do you notice about the number line? How might we use a number line to show a fractional amount? What do you think the whole is? Why? What do you think the line in between 0 and 1 represents? Why? How could we prove that it is one half? (e.g., Measure the distance from 0 to the mark and the mark to 1; fold the number line in half.) Fold the number line to prove the position of the fraction and then mark on one half using standard fractional notation. • What other fractional values could we put on the number line? Where would we put them? Turn and talk to your partner. • W hat values could we add and how do we know where to put them (e.g., One fourth is halfway between 0 and one half, and three fourths is halfway between one half and one whole.) Before we prove exactly where they go, let’s try estimating where we think they might go. Have students point to some spots. Lightly mark them on the number line. Let’s fold the line to see how accurate our estimates are. • Add eighths to the number line following the same line of questioning. • Show another, shorter number line drawn on chart paper with endpoints 0 and 1. Repeat the same line of questioning to add on fractional values. Place the two number lines one above the other and aligned at 0. Why is one half in different places on the two number lines? How can they both represent one half? • Show a third number line that is the same length as the first number line and with hatch marks at the endpoints and the centre. Label the endpoints 0 and 2. What is different about this number line? What do you think the little line in between 0 and 2 represents? Why? Turn and talk to your partner. • Mark 1 on the number line. Where will one half go? Why? Let’s estimate and then fold the line to see how accurate we are. Mark 21 on the number line. What fractional value will go halfway between 1 and 2? Can it be one half? Why not? (e.g., We have already put one half on the number line so this can’t continued on next page Fractions 481
be one half too.) Let’s count the fractions to help us (e.g., 1 one-half, 2 one- halves, 3 one-halves, 4 one-halves; one half, two halves, three halves, four halves; 21 , 22 , 32 , 24 ). Mark these fractions on the number line. name three halves? (e.g., one and one half) How else can we • Let’s look at the position of one half on all three number lines. How is it different and how is it the same? (e.g., One half is different distances from 0, but the relative position of one half is the same on all three lines—it is always halfway between 0 and 1.) So, we must always look carefully at our endpoints to help us place fractions on a number line. 482 Number and Financial Literacy
14Lesson Fraction Art Math Number Curriculum Expectations • B 1.6 use drawings to represent, solve, and compare the results of fair-share Arts problems that involve sharing up to 20 items among 2, 3, 4, 5, 6, 8, and 10 Curriculum sharers, including problems that result in whole numbers, mixed numbers, Expectations and fractional amounts Teacher • B 1.7 represent and solve fair-share problems that focus on determining and Look-Fors using equivalent fractions, including problems that involve halves, fourths, Previous Experience and eighths; thirds and sixths; and fifths and tenths with Concepts: Students have worked Visual Arts with area models by naming and identifying • Elements of design: Colour: colour for expression; mixing of colours with the fractional parts and partitioning wholes into white to make a range of warm and cool tints various fractional parts. • D 1.4 use a variety of materials, tools, and techniques to respond to design challenges Possible Learning Goal • Applies understanding of fractions and equi-partitioning to create a piece of art • Creates sections in an artwork using given proportions with reasonable accuracy • Correctly identifies fractional parts and explains what they mean • Uses correct fractional language to describe the parts • Explains and/or shows the relationship between the fractional parts and the whole PMraotcheesmseast:ical About the rssaPetenrrplaodertbeceplstegrienominegvtsiinst,noogcgol,o,vlrnisnengafel,necdrctetiniangsg,o,ning communicating Students have had several experiences representing fractions with different models, and dividing wholes to create equal shares and expressing the shares as fractions using words. It is important that they see the relevance of fractions in their lives and how the concepts they learn can be applied to other curriculum areas, such as science and visual arts. Fractions 483
Math Vocabulary: About the Lesson wfpaoharueorrtaltiehti,msop,noasidnrixetgstl,h, esh,qauelviagelh,st,hs, The activity consolidates fractional concepts by having students create artwork from instructions that describe fractional parts and their colours. Students can be creative in their designs and reflect on the different possibilities for their artwork. Materials: Minds On (20 minutes) Digital Slide 59: • Show Digital Slide 59: Warm Colours and Cool Colours. Ask students what Warm Colours and Cool Colours, white they notice about the types of colours used in the picture. Ask which colours paper (11 × 17), they think are cool colours and which they think are warm colours. Have markers and/or pencil them justify their reasoning. Ask what the warm colours remind them of crayons, construction (e.g., the sun, fire). Ask what the cool colours remind them of (e.g., water, paper in warm and cool grass). Discuss how art can express feelings and emotions. Explain that colours, BLM 70: artists carefully choose their colours to evoke the feelings they want the Fractions in Art viewer to experience. Time: 2–3 sessions, • Have students estimate what fraction of the artwork uses cool colours. Ask about 50 minutes per session questions such as, “Is more than half of the artwork in cool colours, or is less than half of the artwork in cool colours? Why do you think so? What would need to be changed in the artwork to make it closer to half cool colours and half warm colours?” Have students explain their reasoning. • Ask students to tell you about the use of warm colours in this artwork. Ask how the warm colours make them feel and why they think this is so. Ask what would need to be changed in the artwork for it to show warm colours and cool colours equally. Ask, “Is there more than one way to show half in this image? Do we need to show parts adjacent to each other?” • Tell students that they are going to create their own artwork by following given instructions. Teaching Tip Working On It (30–40 minutes per session) This activity will • Students can work individually or in pairs. If you use this as a consolidating probably take 2 or 3 days to complete. assessment activity, it may be beneficial to have students work individually. Students can work on their piece of art • Students will create a piece of art having four sections, each of which is one throughout the day when they have extra fourth of a white 11 × 17 sheet of paper. Provide paper, markers and/or time and/or in art pencil crayons, and construction paper in warm and cool colours. class, since it covers expectations from the • Have each student fold a 11 × 17 sheet once vertically and then once grade three visual arts curriculum. horizontally to create the four sections. Read over all the instructions on BLM 70: Fractions in Art as a class and ensure students understand all the directions and vocabulary. Explain that they can estimate the fractional amounts and they do not have to be exact. Emphasize that all the space in each section must be filled in with warm or cool colours. • Students can colour in the parts in each section, or they can cut out the parts from coloured paper and glue them onto the sections. 484 Number and Financial Literacy
• On a separate piece of paper, have students write the whole and the fractional parts (e.g., warm colours and cool colours) of each section. Differentiation • You may want to adjust how many different sections students are designing. For example, you may want them to follow the instructions for only one section to fill the entire 11 × 17 sheet, or follow instructions for two sections on a piece of paper divided in half. Students could also choose their own challenge. • Students who want more of a challenge can use equivalent fractions for any of the sections. (e.g., They could make one half as four eighths.) • You could have students divide their four sections in a different way (e.g., in long rectangular bars of equal size). • You may want to add more parameters to some of the descriptions of the sections (e.g., the two sixths in Section 2 cannot be touching). Assessment Opportunities Observations: • Check whether students can equally partition with reasonable accuracy. • Can students identify the fraction in relation to the whole? • Can students name the fractional parts they have created in each section using the warm and cool colours? Conversations: Use prompts similar to the following: – How did you create equal parts in your section? What is important to show in this section? Can you think of another way to divide your shape rather than drawing a line? (e.g., folding) – What can you tell me about the fractions you have represented using warm and cool colours in this section? Consolidation (15 minutes) • Hang up students’ artwork and have a gallery walk. • As a class, ask how all the art is the same (e.g., same fractional parts) and how it is different (e.g., parts are organized in different ways). • Select two or three pieces to analyse as a class. Ask students if the pieces make them feel warm or cool overall. Discuss whether this is because of the amount of cool and warm colours on the page or the way in which the colours have been used. (e.g., All cool colours in the middle, surrounded by warm colours, evokes a cool feeling.) • B uilding Social-Emotional Learning Skills: Self-Awareness and Sense of Identity: Have a discussion about fractions in general and the activities they have worked on throughout the unit. Ask what activities they enjoyed the most and why. Ask what they learned about fractions and what they found most interesting. Ask what they still wonder about fractions and what Fractions 485
they would like to learn more about. Ask how they feel as learners, from the beginning of the unit to the end. Ask what they think helped them understand fractions better. Ask what they still find confusing. Make a list of some of their ideas. Over the next couple of weeks, take 5–10 minutes to review and reinforce one of the concepts on the list. Regularly refer to it so students can see their progress by having practice sessions. In this way, students see that the learning does not end when a unit is over and that there are other opportunities to improve during the year. Further Practice • R eflecting in Math Journals: Verbally pose one/some of the following prompts: – U se pictures, numbers, and/or words to show what you have learned about fractions. – U se pictures, numbers, and/or words to show which fraction activity you liked the best. Why did you like it? – U se pictures, numbers, and/or words to show how you feel about learning fractions and what interests you most. 486 Number and Finacial Literacy
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Lawson, A. (2015). What to look for: Understanding and developing student thinking in early numeracy. Toronto, ON: Pearson Canada. McIntosh, A. Reys, B. J., & Reys, R. E. (1992, November). A proposed framework for examining basic number sense. For the learning of mathematics, 12(3), 2–8. Ontario Ministry of Education. (2010). A sound investment: Financial literacy education in Ontario schools. Toronto, ON: Queen’s Printer for Ontario. Ontario Ministry of Education. (2014). Paying attention to fractions K–12. Support document for Paying attention to mathematics education. Toronto, ON: Queen’s Printer for Ontario. Ontario Ministry of Education. (2016). A guide to effective instruction in mathematics, Grades 1 to 3: Number sense and numeration revised. Toronto, ON: Queen’s Printer for Ontario. Ontario Ministry of Education. (2018, April). Fractions across the curriculum. Capacity Building K–12, Special Edition #47. Toronto, ON: Queen’s Printer for Ontario. http://www.edu.gov.on.ca/eng/literacynumeracy/inspire/research/ fractions_across_curriculum.html Ontario Ministry of Education. (2020). Mathematics (2020). Ontario Curriculum and Resources website. https://www.dcp.edu.gov.on.ca/en/ curriculum/elementary-mathematics Petit, M., Laird, R., & Marsden, E. (2010). A focus on fractions: Bringing research to the classroom. New York, NY: Routledge. Small, M. (2005). PRIME: Number and Operations. Toronto, ON: Thomson Nelson. Small, M. (2009). Making math meaningful for Canadian students, K–8. Toronto, ON: Nelson Education. Van de Walle, J. A., & Lovin, L. H. (2006a). Teaching student-centered mathematics: Grades K–3. Boston, MA: Pearson. Van de Walle, J. A., & Lovin, L. H. (2006b). Teaching student-centered mathematics: Grades 3–5. Boston, MA: Pearson. 488 Number and Financial Literacy
Number & Financial Literacy Teacher’s Guide Part of Math Place Grade 3 Lead Author: Diane Stang, National Math Consultant for Scholastic Education Additional writing by: Jennifer Fannin, Toronto District School Board Laura Inglis, Toronto District School Board Jane Silva, Toronto District School Board Lynnette Werner, Halton District School Board Math Reviewer: Lynnette Werner, Halton District School Board Indigenous Consultant: Bryan Bellefeuille, Nipissing First Nation Director of Publishing: Molly Falconer Project Manager: Jenny Armstrong Editors: Jackie Dulson, Dimitra Chronopoulos, Sundus Butt Proofreader: Danielle Arbuckle Art Director: Kimberly Kimpton Designer: Dennis Boyes Production Specialist: Pauline Galkowski-Zileff Copyright © 2022 Scholastic Canada Ltd. 175 Hillmount Road, Markham, Ontario, Canada, L6C 1Z7 ISBN: 978-1-4430-5402-7 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, scanning, recording or otherwise, without the prior written consent of the publisher or a license from The Canadian Copyright Licensing Agency (Access Copyright). For an Access Copyright license, call toll free to 1-800-893-5777.
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