# Alaska Mathematics Standards Math Tasks Grade K Going on a Shape Hunt Naming and Identifying Shapes

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3 Students often mistake a change in size or orientation of a shape as a change in the name of the shape. One of the most common misconceptions in geometry is the belief that orientations are tied to shape. A student may see the second of the figures below as a triangle, but claim to not know the name of the first. Students need to have many experiences with shapes in different orientations. For example, ask students to form other triangles with the two triangles in different orientations. Formative Assessment Questions: How many shapes did you find? What types of shapes did you find? Did you find different kinds of the same shape? How can you describe the shapes that you found? What shapes were the easiest to find? Hardest? Differentiation: Extension Send home copies of the Two-Dimensional Task Sheet or the Three-Dimensional Task Sheet and have students go on a shape hunt at home. Allow students (with supervision) to use a digital camera to take pictures of all the shapes found in your classroom or your school and create a book of shapes. The book could have a section for each shape and each student could be responsible for writing the text for one page of the book. Have students pair up and visit the Sammy s Shapes website where they can identify specific shapes appropriate for their grade level and locate and describe the shapes. This website can be used during math work stations or center time. Intervention Give the child a picture of a space with shapes highlighted, for example: a picture of a grocery store aisle with the outline of the cereal box bolded. Have them place cut outs or manipulatives on top of the outline. Vocabulary: Circle Square Rectangle Hexagon Triangle Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 3 of 49

5 Part II Give each student 2-3 index cards. Have students go on a geometric solid shape hunt in the classroom to fill in the last column of the Touch It, Count it, Chart It, chart. Students tell the name of the solid it represents, write its name on an index card, and attach it to the item. Shapes can then be displayed in a Solid Shapes Museum. As you circulate, observe the student s choices and listen to their conversations. Help students to understand they can learn to recognize the shapes even though they are not exactly the same as the model. During their shape hunt, and as students share their 3-D findings, ask the students questions such as: Is this object exactly like our model? How is it the same? How is it different? Which solid is the hardest to find in the classroom? Why? What do you notice about the faces of the objects? (SMP 1, 3, 5, 6, 7) Teacher Reflection Questions: Are students able to talk about where we find shapes in the real world? How are the students describing the shapes they are finding? Are they able to identify something easily from the classroom without referring back to the solid example? Do most students choose the solid they are most familiar with, such as a rectangular prism? Which ones are they not choosing? Number Talk: There is not a number talk available that is appropriate for this task. Background Knowledge/Common Misconceptions: Students often use incorrect terminology when describing shapes. For example, students may say a cube is a square or that a sphere is a circle. The use of twodimensional shape names that appear to be part of a three-dimensional shape in order to name the three-dimensional shape is a common mistake. For example, students might call a cube a square because the student sees the face of the cube. Work with student to help them understand that the two-dimensional shape is a part of the object, but it has a different name. Another common misconception is separating a square from the identified category of rectangles. A square exhibits the same characteristics of rectangles, however it is special rectangle because it sides are equal in length. Students often mistake a change in size or orientation of a shape as a change in the name of the shape. One of the most common misconceptions in geometry is the belief that orientations are tied to shape. A student may see the second of the figures below as a triangle, but claim to not know the name of the first. Students need to have many experiences with shapes in different orientations. For example, ask students to form other triangles with the two triangles in different orientations. There are both 3-D (solid) and 2-D shapes (flat) shapes. Students should have a beginning understanding of the difference in sides and faces. One way to explain how 3-D shapes are different from 2-D shapes is through discussion. 3-D shapes have a solid body. This is why it is easy hold them in our hand. 2-D shapes are flat, which is why it is easy to draw them on paper. If you use the term solid when talking about 3-D shapes, then discussing face on the 3-D shape is a little easier. Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 5 of 49

6 It is natural for students to initially talk about the faces as sides but as you talk about them use the word face, not side. Gradually the students will pick up on this and will start calling the sides faces. Formative Assessment Questions: How would you describe a solid shape? What solid shapes do you see in the classroom? Playground? Home? Differentiation: Extension Students could determine attributes and then use that information to graph objects from the Shape Museum. Students could extend their search to the rest of the school and /or use cameras to take pictures of other items that represent 3-D solids. A home connection could be made by sending a parent letter asking students to search for solids they could bring back to school to add to the Shape Museum. Have students use modeling clay or play dough to create some of the solids they identified as they search the classroom. Students can use a model shape to replicate, or compose the shape from memory. Intervention Give struggling students cards with examples of 3-D solids that can be used when they are looking for objects for the Shape Museum. Vocabulary: Face Cylinder Cone Cube Sphere Corner Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 6 of 49

9 Background Knowledge/Common Misconceptions: Students often use incorrect terminology when describing shapes. For example, students may say a cube is a square or that a sphere is a circle. The use of twodimensional shape names that appear to be part of a three-dimensional shape in order to name the three-dimensional shape is a common mistake. For example, students might call a cube a square because the student sees the face of the cube. Work with student to help them understand that the two-dimensional shape is a part of the object, but it has a different name. Another common misconception is separating a square from the identified category of rectangles. A square exhibits the same characteristics of rectangles; however it is special rectangle because its sides are equal in length. Students often mistake a change in size or orientation of a shape as a change in the name of the shape. One of the most common misconceptions in geometry is the belief that orientations are tied to shape. A student may see the second of the figures below as a triangle, but claim to not know the name of the first. Students need to have many experiences with shapes in different orientations. For example, ask students to form other triangles with the two triangles in different orientations. The students should have prior knowledge of solid geometric shapes and the vocabulary used to describe these shapes. Students will draw and name solid geometric shapes of a cube, cylinder, sphere, and cone and list the number of faces, edges, and vertices/corners of each figure. Formative Assessment Questions: How many toothpicks would you need to build a? What makes shapes different from each other? How do shapes fit together and come apart? How are these shapes different from one another? How are they alike? What is the difference between flat and solid? Differentiation: Extension Have students create the largest possible 3-dimensional shape they can make. Have students make different types of triangles (scalene, isosceles, right, equilateral), and quadrilaterals (rectangle, square, rhombus, trapezoid, etc...). The key here is that shapes must be different not by size but by attributes. Intervention Allow students to use straws or pipe cleaners to create shapes. Give students models of the shapes and have them reconstruct the shape they see. Vocabulary: Solid 3-D Shape Flat Shape Line Segment Square Rectangle Triangle Cube Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 9 of 49

11 Dot Flash: Teacher/Student flashes a dot card to class/partner and quickly covers it up. Students must say the quantity of dots they saw and describe how they know what they saw. Example: I saw 4 dots because I saw a group of 3 dots and there was one left over to make 4.The difficulty in the game can be increased by the amount of time that the dots are shown to students. (SMP 1, 3, 6, 7) Count Em: A card is turned over. The first player to say the quantity of dots on the cards keeps that card. Partner must count the dots on the card to verify. No assuming. (SMP 6, 7) One More/Less: Same as dot flash but students need to say either 1 more or less than the dots on the card. Whether it is more or less must be established before the game begins. (SMP 1, 3, 6, 7) Who Has More/Less/Same?: 2 players turn over 1 card at the same time. The first player to identify which card has more/less/same keeps the 2 cards. (SMP 3) Line Em Up: Give a student a set of cards and have them line the cards up in a specific order: least to greatest forward counting sequence, greatest to least backward counting sequence. (SMP 1, 3, 6, 7) Kindergarten students are extremely creative and continuously invent new games. Have students create a game using the cards and share with classmates. Van de Walle s Teaching Student Centered Mathematics K-3, lists numerous ways to incorporate subitizing activities into the classroom. A greater variety of dot cards and dot plates can be found online and Van de Walle s Blackline Masters Series at: In addition Van de Walle suggests numerous ways that activities and tasks can be repeated throughout the school year as centers or stations. Teacher Reflection Questions: Are students able to rote count accurately? Are students able to count dots with one-to-one correspondence? Are students able to subitize? Are students able to compare quantities to determine more, less, or same? Are students able to line cards up in a specific order (least to greatest forward counting sequence or greatest to least backward counting sequence)? Number Talk: Dot Images: Showing students an organized arrangement of dots for a few seconds and then asking them to share how many they see encourages subitizing and fluency. Incorporating dot images into classroom number talks provides opportunities for students to work on counting, seeing numbers in a variety of ways, subitizing and learning combinations. The following dot image number talk consists of three problems that are to be given sequentially. As each problem is shown, ask students, How many dots do you see? How do you see them? As the child is telling you what they see, connect the child s thinking to a number sentence by circling the dot arrangement the child describes and writing a correlating number sentence. Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 11 of 49

15 Formative Assessment Questions: What number did you roll? How many counters do you have in your chute right now? What number do you need to roll to fill your chute? Which chute has the most? Least Differentiation: Extension Change the value of each space to 10 and have students skip count by 10 to 100. Note: the chute won t be filled if students play to 100. After students are familiar with skip counting forward by tens they may alternate rolls to skip count backwards and forwards. You may also make a version with no individual spaces instead the playing board would consist of columns. This allows for a variety of counters to be used, including paper clips, pennies, etc. Use only one type of counter when playing, of course! Intervention Because the students must say the total number of counters out loud, the numerals for each space could be written on the game board to help with number recognition and counting forward and backwards. Vocabulary: Most Least References: Parrish, Sherry. Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K 5. Sausalito: Math Solutions Publications, 2010 Van de Walle, John A., and Lou Ann H. Lovin. Teaching Student-Centered Mathematics: Grades K-3, Volume 1. Pearson, 2006 Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 15 of 49

17 Comment: There are 2 versions of this game. Each version can be played with more/less 1 OR more/less 2. The spinners provided can be used or dice/wooden blocks can be used to take place of the spinners. The following description is generic for both games. Player 1 rolls the die (1-6) or (4-9) and spins the spinner (more/less or more/less 1&2). The player covers the number which represents the die and the spinner combined. Part I (More/Less): Example: if player 1 rolls a 5 and then spins less, they can cover any number less than 5. (4, 3, 2, 1 or 0) Watch the number the student covers as it relates to covering 3 in a row. Are they randomly picking a number to cover? Or are they choosing the number to cover based on their best chance to cover 3 in a row? (SMP 1-8) Part II (More/Less 1&2): Example: if you roll a 5 and spin 2 more, you count forward 2 from 5 to end at seven. As students play, they record the number they rolled on the recording sheet. Then they record what they spun (more/less, 1 more, 1 less, etc...). Students then record what they covered on the game board. They justify this in the because section by writing an equation or another justification for covering. (Example: A player could say she rolled one more than 8. That s 9, because one more is the next number, so in the space she wrote it s next. ) First player to get 3 counters in a row wins. (SMP 1-8) Teacher Reflection Questions: Are students able to identify numbers 0-10? Are students able to identify 1 more or less than a given number? Are students able to identify 2 more or less than a given number? Are students able to write numerals correctly? Number Talk: Five and Ten Frames can be used to foster fluency, subitizing, working with place value, and computing with addition and subtraction. Varying the questions posed to students can change the purpose and focus of each ten-frame. Questions such as: How many more do we need to make ten? How many are left after removing three? are great computation questions that compliment this More or Less task. Five-and-ten frames can be used as a single row of five (five-frame), two rows of five (ten-frame), or as two ten-frames together to provide the opportunity to work with numbers to twenty. Five and ten-frame number talks are each designed to be used in a single session, in any order. The focus for the numbers 3 to 9 is to ask students, How many dots do you see? How do you see them? With frames for the number 10, the question shifts to, How many more to make ten? Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 17 of 49

18 Example: As each number talk is shown; ask students, How many more do we need to make ten? How many are left after removing?" Additional examples of five-and-ten frames can be found in Number Talks by Sherry Parrish (pgs ). Background Knowledge/Common Misconceptions: Some students might not see zero as a number. Ask students to write 0 and say zero to represent the number of items left when all items have been taken away. Avoid using the word none to represent this situation. Some students might think that the count word used to tag an item is permanently connected to that item. So when the item is used again for counting and should be tagged with a different count word, the student uses the original count word. For example, a student counts four geometric figures: triangle, square, circle and rectangle with the count words: one, two, three, and four. If these items are rearranged as rectangle, triangle, circle and square and counted, the student says these count words: four, one, three, and two. The concept of more, less and the same are basic relationships contributing to the overall concept of number. Children begin to develop these ideas before they begin school. Children entering kindergarten can almost always choose the set that is more if presented with sets that are quite obviously different in number. Formative Assessment Questions: How do you know that you counted correctly? What does more mean? What does less mean? What numbers do you need to win? Why did you choose that number? If you spun 2 more what number would you need to roll to win? Differentiation: Extension Have the students model their actions using a ten-frame or Rekenrek. This will also help students to record their actions. Intervention Allow the students to model with a ten frame or through the use of a number line. Vocabulary: More Less References: Parrish, Sherry. Number Talks: Helping Children Build Mental Math and Computation Strategies, Grades K 5. Sausalito: Math Solutions Publications, 2010 Adapted from Georgia Department of Education, CCGPS Math Framework, All Rights Reserved. Page 18 of 49

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