The Long And Short Of It - Math Unit - Trinity Western University
The LONG and short of it. A grade one math unit on non-standard measurement.
Table of Contents Thematic Statement 3 Core Competencies 4 Learning Standards 5 Assessment Strategies 7 Assessment Rubrics 9 The Learning Plan 10 Weekly Calendar 14 Curriculum Resources 15 Learning Routines 16 Appendix A: Learning Plans 17 Appendix B: Handouts, Student Samples, and Assessment 18 2
Thematic Statement Measurement is a part of everyday life. We use measurement when following recipes to cook or bake, we measure distance either around a track or across the city, and we use it to tell how tall or short someone is. We use different forms of measurement from standard to non-standard all over the world. Whether students are aware of it yet or not, they use measurement in their classroom, at home, and when they are out on the playground. This unit will help students to become aware of ways they already engage in measuring and ways they can grow and develop in their skills. Students will already have a beginning knowledge of addition and subtraction which will help them calculate measurements and they will have acquired skills in more than and less than understanding the idea of something that is bigger, or smaller. These are the foundational skills that students will be entering with. In this 4-week unit students will explore measurement specifically related to length using non-standard units. We will briefly touch upon measurement with perimeter and cups as well as a beginning understanding of standard units of measurements. Students will develop and learn the skills needed to measure through exploring hands on activities. This unit will focus on two big ideas, that measurement helps in comparing and identifying different objects and that measurement helps to know the size, amount or length of an object. Students will seek to answer questions that identify why measuring is important and useful in their everyday lives, and how measurement helps them solve problems. Over the course of this unit students will becoming familiar with measurements and its many facets. Students will begin with comparing objects according to their attributes in regard to size. This will give them the beginning understanding of identifying different sizes and the academic vocabulary like smaller, bigger, longest, shortest, that is needed to develop in their understanding of measurement. They will explore using non-uniform measurement and then move to uniform units of measurement. Students will have opportunity to explore through inquiry groups, math centers and a lesson connecting nature and the world around them to measurement. Students will express their learning through partner activities, having the opportunity to measure each other, things in the classroom and obscure items. Students will learn to problem solve, choosing the proper materials to measure and figuring out what works best to get an accurate measurement. Students will demonstrate their understanding at the end of the unit with a final product which will demonstrate their skills of estimating, measuring with non-standard and standard units. 3
Core Competencies Core Competencies Critical Thinking: Question and Investigate Student Self-Assessment Core Competency I can ask open ended questions and gather information. I can explore materials and actions. I can consider more than one way to proceed in an investigation. Student Self-Assessment Strategy Red, Yellow, Green Journal/Picture Reflection Self-reflection sheet Description I will give students a clothes pin with their name on it. I will have them attach it to a box that says I really get this (green), I kind of get this(yellow), or I don’t get this(red). Have students draw a picture of all the different objects they have used to measure. Have them write a journal entry on what objects they have used and what they would still like to try. Students will be provided a sheet that lists the 5 things that are needed to measure accurately. They will circle if they consider these things never, sometimes or always with emotion faces. 4
Desired Learning Intentions Learning Intentions Big Ideas Learning Outcomes Enduring Understandings Students will understand that Essential Questions Students will keep considering Curricular Competencies Students will be able to Content: Students will know how to Enduring Understanding #1 Enduring Questions: D1 Estimate reasonably (to do)* Measurement helps me compare and identify different objects C1 Develop and demonstrate an EQ1: What similarities and differences do I see in the size of understanding of measurement through play inquiry (to create) things around me? K1 Sort objects using one attribute and explaining the rule. EQ2: How does being able to compare and describe objects help me in my everyday life? V1 Connect an understanding of lengths and size to daily life and the world around (to value) K2 Compare lengths and size in comparison to something else (bigger, smaller, longer, shorter) Learning Standards LS1 Estimate lengths of objects using sight, vocabulary including bigger, smaller. (D1, K2) LS2 Assess how being able to compare sizes and lengths is useful in my daily life and world. (V1, K2) LS3 Develop and demonstrate an understanding of object length and size through play inquiry. (C1, K2) 5
Big Ideas Enduring Understandings Students will understand that Enduring Understanding #2 Essential Questions Students will keep considering Enduring Questions: Measurement helps me to know the size, amount or length of an object. Learning Outcomes Curricular Competencies Students will be able to Content: Students will know how to K3 measure using standard units EQ3: What can I use to measure something? D2 Estimate reasonably (to do) * C2 Apply an understanding of measurement through play inquiry (to create) EQ4: Why is measuring important and what is it useful for? D4 Develop and apply an understanding of measurement through problem solving (to do) K4 measure using non-standard units (cubes, paper, clips, hands) D5 Develop and use multiple strategies to engage in problem solving V2 Connect measurement to each other and the world around you (to value) Learning Standards LS4 Estimate lengths reasonably using non-standard and standard measurement. (D2, K3, K4) LS5 Develop and use multiple measurement strategies to engage in problem solving. (D5, K3, K4) LS6 Apply an understanding of non-standard and standard units through problem solving. (D4, K3, K4) LS7 Develop an understanding of measuring with non-standard and standard units through play inquiry. (C2, K3, K4) LS8 Connect measurement to each other and the world around you. (V2) 6
Evidence of Student Learning Of Learning: Culminating Performance Tasks Learning Standards Estimate lengths reasonably using non-standard and standard measurement. (D2, K4, K5) Apply an understanding of nonstandard and standard units through problem solving. (D4, K3, K4, K5) Assessment Strategies Final Project Final Project Description Students will trace their feet and cut them out. They will then estimate how many of a non-standard unit long their foot would be and then estimate how many of a standard unit long their foot would be and write it down on their paper. Using their cutout feet students will be able to choose from a variety of non-standard and standard unit objects and they will choose which to use and how to use it to measure their feet and write in on their sheet. They will have to display an understanding of how to measure and choose the appropriate measuring tool. For Learning Learning Standards Estimate lengths of objects reasonably using sight, and vocabulary including bigger, smaller. (D1, K2) Develop and use multiple measurement strategies to engage in problem solving. (D5, K4, K5) Assessment Strategies Observation and exit tickets Conferencing Description I will have a sheet to record observations, throughout this unit, on whether students are estimating reasonably. I will also provide exit tickets asking students a simple question about estimating and have them jot an answer to give to me. I will sit down with each student, providing them something to measure and multiple objects that could be used, and have them talk me through their strategy on how to measure the object. 7
As Learning Learning Standards Develop and demonstrate an understanding of object length and size through play inquiry. (C1, K2) Assess how being able to compare sizes and lengths is useful in my daily life and world. (V1, K2) Develop an understanding of measuring with non-standard and standard units through play inquiry. (C2, K4, K5) Connect measurement to each other and the world around you. (V2) Assessment Strategies Description Red, Yellow, Green At various points during play inquiry times I will have students take a clothes pin with their name on it and put it on the red if they really don’t get it and need help, yellow if they sort of get it, or green if they really get it. This will help students to stop for a minute and recognize that although we are playing there is a goal. Pair Share Students will share with each other 2-3 ways that comparing sizes and length is useful in their daily life and the world. Red, Yellow, Green At various points during play inquiry times I will have students take a clothes pin with their name on it and put it on the red if they really don’t get it and need help, yellow if they sort of get it, or green if they really get it. This will help students to stop for a minute and recognize that although we are playing there is a goal. Self-reflection sheet They will color an emotion face in response to 3-4 I can statements and then at the bottom draw a face that represents how they feel about understanding these things. 8
Assessment Rubrics Project: How long is my foot? Students will trace their foot and put it on the poster. They will then demonstrate their skills of estimating, choosing proper materials and measuring accurately using non-standard and standard measurements of the foot. Learning Standards: Estimate lengths reasonably using non-standard and standard measurement. (D2, K4, K5) Apply an understanding of non-standard and standard units through problem solving. (D4, K3, K4, K5) Approaching Areas for Growth Criteria Standards for This Performance Advanced Evidence of Exceeding Standards Reasonable Estimation: Estimates length reasonably using non-standard and standard units. Adequate Tools: Shows evidence of problem solving by choosing the proper measuring tools. Accuracy (non-standard): Accurately uses non-standard units to measure foot. Accuracy (standard): Accurately uses standard units to measure foot. Comments: 9
The Learning Plan ** These two learning standards will be encouraged throughout every lesson ** Estimate lengths of objects using sight, vocabulary including bigger, smaller. (D1, K2) Estimate lengths using non-standard and standard measurement. (D2, K4, K5) Week 1: Inquiry through comparing and non-uniform, nonstandard units Enduring Understanding: Essential Questions: EQ1: What similarities and differences do I see in Measurement helps me compare and identify the size of things around me? different objects EQ2: How does being able to compare and describe objects help me in my everyday life? Learning Standards: Estimate lengths of objects using sight, vocabulary including bigger, smaller. (D1, K2) Assess how being able to compare sizes and lengths is useful in my daily life and world. (V1, K2) Develop and demonstrate an understanding of object length and size through play inquiry. (C1, K2) Develop an understanding of measuring with non-standard units through play inquiry. (C3,K4, K5) Develop and use multiple measurement strategies to engage in problem solving. (D5, K4, K5) Learning Event Details - A unit hook where students will have an opportunity to grab an object out of a bag and describe its size. 1. Mystery Bag - Vocabulary to describe can be given to those who need extra help ie: bigger smaller, and a comparison can be added to those who need an extra challenge. - Will need a bag with 22 objects of varying sizes. - An inquiry based lesson where students will be given multiple questions to help grow their understanding of comparing sizes. For example, what can you find in the classroom that is about the size of 2. Compared to what? your arm? -An adaptation would be to ask for something that is shorter than or longer than instead of about the same length. -Curriculum resourcing being used is “Great Ways to Differentiate Mathematics Instruction” - This lesson will have 4 stations where students will have the opportunity to explore measuring with non-standard units. They will be encouraged to figure out ways to measure accurately. Students will choose how they display their findings as they measure. There 3. Your Size, My Size will be a discussion at the end discussing strategies and objects used to measure. -Mix students up so stronger students are grouped with struggling students to perhaps model exploring measurement. - Will need various objects to measure with, and objects to measure 10
Week 2: Inquiry through uniform and standard units. Enduring Understanding: Essential Questions: Measurement helps me to know the size, amount or length of an object. EQ3: What can I use to measure something? EQ4: Why is measuring important and what is it useful for? Learning Standards: Develop and use multiple measurement strategies to engage in problem solving. (D5, K4, K5) Develop an understanding of measuring with non-standard and standard units through play inquiry. (C3,K4, K5) Apply an understanding of non-standard and standard units through problem solving. (D4, K3, K4, K5) Learning Event 1. Teach me to measure 2. Centimeters 3. Ruling measurements 4. Measure a Friend Details - This lesson will start of the week teaching students the proper ways to measure, don’t overlap objects, use one object repeatedly, no gaps between object. Students will make a chart with the teacher. - A chart paper where we write down the rules in word and picture form that students understand. - In this lesson students will learn how to use a rule and develop a beginning understanding of centimeters. Students will do an activity sheet that clearly demonstrates centimeters to practice their knew understanding. - As an extension if students finish early they can go around with a friend measuring objects and discussing if they get the same answer or different and why. - Curriculum Resource Prism Math pg. 89, 22 rulers, 22 activity sheet - This lesson will have 4 stations where students will have the opportunity to explore measuring with uniform and standard measurements after learning proper ways to measure. Students will choose how they display their findings as they measure. There will be a discussion at the end discussing why it’s important to have a standard unit of measurement. -Mix students up so stronger students are grouped with struggling students to perhaps model exploring measurement. - Will need various objects to measure with, and objects to measure, 22 rulers - Students will be put in groups where they will need to measure each person in the group using one non-standard object. They will first estimate who is the tallest and who is the shortest. After measuring and recording their measurements they will identify in order shortest to tallest. - An extension would be to measure using centimeters as well. - Will need chart paper to record answers, measuring objects and markers. 11
Week 3: Exploring Different Kinds of Measurement Enduring Understanding: Essential Questions: Measurement helps me to know the size, amount or length of an object. EQ3: What can I use to measure something? EQ4: Why is measuring important and what is it useful for? Learning Standards: Apply an understanding of non-standard and standard units through problem solving. (D4, K3, K4, K5) Develop and use multiple measurement strategies to engage in problem solving. (D5, K4, K5) Develop an understanding of measuring with non-standard units through play inquiry. (C3,K4, K5) Connect measurement to each other and the world around you. (V2) Learning Event 1. Perimeter 2. Measuring Liquids 3. Measuring a Recipe Details -Students will explore the idea of perimeter. They will be given different shapes and through inquiry will try different ways to measure. - An extension will be to challenge students to try using addition to figure out perimeter rather than counting every side. An adaptation would be to reinforce the strategy of counting on. -Will need shapes, string, rulers, objects to measure with - Students will have an opportunity to play around with measuring water. They will begin inquiry into different size cups holding different amounts. They will learn the standard measurement of liquid. - Students who struggle with the concept can stick to whole cups, whiles those who need a challenge can play around with ½ cups. - different size measuring cups, water - Students will be split into groups and be given the ingredients for a recipe, as a group they will need to measure accurately to create the recipe. -an adaption will be that smaller units like tsp and TBS will already be measured out. - a recipe, ingredients, utensils, 12
Week 4: Closing Lessons and Cumulative Assessment Enduring Understanding: Essential Questions: Measurement helps me to know the size, amount or length of an object. EQ3: What can I use to measure something? EQ4: Why is measuring important and what is it useful for? Learning Standards: Apply an understanding of non-standard and standard units through problem solving. (D4, K3, K4, K5) Develop and use multiple measurement strategies to engage in problem solving. (D5, K4, K5) Develop an understanding of measuring with non-standard units through play inquiry. (C3,K4, K5) Connect measurement to each other and the world around you. (V2) Learning Event 1.Crooked Paths 2. How Long is my foot? Part 1 3. How Long is my Foot? Part 2 4. Outside/Aboriginal Measurement Details - Students will engage in problem solving in applying their knowledge and figure out how to measure something that is not straight. They will be given, curvy lines and will have to use problem solving to figure out how to measure them. -An extension would be to have to use centimeters to figure out the length of the line. An adaptation would be to provide students with one unit to use, so that they are focusing on how to measure rather than what to measure with. -Paper with curvy lines, various objects to measure with, rulers - Students will trace their feet and cut them out. They will then estimate how many of a non-standard unit long their foot would be and then estimate how many of a standard unit long their foot would be and write it down on their paper. -Adaptation will be for students not to have to do standard units. - Paper, scissors, sentence frames - Using their cutout feet students will be able to choose from a variety of non-standard and standard unit objects and they will choose which to use and how to use it to measure their feet and write in on their sheet. They will have to display an understanding of how to measure and choose the appropriate measuring tool. -Adaptation will be for students not to have to do standard units. - Various measurement tools -Students will be taken outside to explore how measurement is found in the world around them. They will explore the use of Aboriginal measurement like wing span, palm, and digits. This will be a closing and reflective lesson. 13
Weekly Calendar Week Monday Tuesday Wednesday Thursday Friday 1 January 29 January 30 January 31 February 1 February 2 Mystery Bag 100’s Day Compared to what? My size your size. Math Centers February 5 February 6 February 7 February 8 February 9 Teach me how to measure Centimeters Ruling Measurements Measure a Friend Math Centers February 12 February 13 February 14 February 15 February 16 Perimeter Measuring Liquids Measuring a Recipe Math Centers February 21 How long is my Foot? February 22 Outside/ Aboriginal Measurement February 23 Pro-D-Day 2 3 Family Day 4 February 19 Crooked Paths February 20 How Long is my Foot? 14
Curriculum Resources Resources Math Quest by Kelly Wortzman Jump Math 1.1 Active Mathematics Activity Cards Prism Math Mcgraw-Hill Ryerson Purpose Activity Sheet that will be used for math centers of as formative information for me. Activity sheets that will be used for math centers of as formative information for me. Math Centers/Early Finishers Centimeters activity sheet that lays out centimeters in a clear and engaging way. Literature to connect to lesson ideas Literature to connect to lesson ideas The royal treasure measure by Harris, Trudy Size: Many ways to measure by Michele Koomen Measuring with Sebastion Pig and friends on Literature to connect to lesson ideas a road trip by Jill Anderson 15
Learning Routine Math Centers Friday’s for 30-40 min Big Ideas Measurement helps me compare and identify different objects. Measurement helps me to know the size, amount or length of an object. Core Competencies Critical Thinking: Question and investigate I can explore different ways to sort objects based on size. I can experiment with different ways of measuring. I can explore what is needed to measure accurately. Learning Standards LS1. LS2, LS3, LS4, LS5, LS6, LS7, LS8 Description Math centers are a new routine that will be introduced when this unit starts. It is aimed to increase the amount of inquiry time as well as provide ample opportunity for students to explore what they are learning on a deeper level. The centers will include activities that encourage use of different measuring objects, practice estimating and encouraging problem solving on how to measure obscure objects. Each week the centers will change to emphasize the learning of the week. Math Inquiry Titles Make a Garage: Make a garage with blocks, how many cards fits, make a garage that will fit 3, or 4 cards. This station will be the beginning foundation of using sight and estimating to make something big enough to hold a certain number of cars. Find Two Things That are the Same Length: Look around the room for two things that are the same length, measure to check, draw a picture of what you found. Make a Paper Chain: Students will be challenged to make a paper chain as long as something else, at the end the group will order their chains from smallest to largest Your Family: Students will use playdough to make all the people in their family. They will then order them from tallest to shortest Measuring Your Body: Students will try measuring different parts of your body, waist, arm, foot with a string and then paste the strings in order from shortest to longest on the paper. Can You Find: Fill out a sheet that asks for students to find something that is 6 paperclips long, 10 paper clips long, 1 strong long and they will write or draw what they found. How many footsteps: Students will trace their foot and use it as a form of measurement. They will record how many footsteps from different places. Use a Ruler: Students will be encouraged to practice measuring things with a ruler. They will record what they measured and the length in cm. Make a Tape Measure: Students will be asked to make a tape measure using their own unit of measurement, blocks, pencils, hands. They will then use that tape measure to measure things in the class. Which has the Longest Perimeter: Students will explore measuring around things. They will choose their unit of measurement and then compare the perimeter of a few objects. Make the Longest Snake: Students will make a few snakes of different lengths and then order the snakes from longest to shortest. Water Tray: Students will be at a water station playing with different containers and amounts of water. They will be encouraged to find two containers that hold the same amount of liquid or more or less than. Resources Math Quest by Kelly Wortzman Jump Math 1.1 Active Mathematics Activity Cards Assessment Assessment AS: Students do these activities by themselves and we ask students beforehand to think about a skill that they think they need to practice more or work on more, it is up to them to practice or use the activity that will best help them and further their own learning. Assessment FOR: There will be a few activity sheets or recordings during the stations that we will collect and see where students are at, and what skills they still need to develop or practice. 16
Appendix A Math: How does it compare? Learning Experience Number: 1 Length of Learning Experience: 20-25 min Curriculum Area: Math Curriculum Plan: Comparing Sizes Core Competencies Critical Thinking Question and investigate I can explore different ways to sort objects based on size. Big Idea: EU 1: Measurement helps me compare and describe different objects. EQ1: What similarities and differences do I see in the size of things around me? EQ2: How does being able to compare and describe objects help me in my everyday life? Know/Do/Value – What does this look like? LS3 Develop and demonstrate an understanding of object length and size through play inquiry. (C1, K2) Students are able to look at an object and begin to use appropriate vocabulary to describe its size. Using words like smaller, larger, taller, shorter, bigger. Student Friendly Version of Intended Learning Standards/Curricular Competencies and Content: I can compare length and size of objects. Flexible Learning Context: First Peoples Principles of Learning: Learning is holistic, reflexive, reflective, experiential and relational (focused on connectedness on reciprocal relationships and a sense of place). Students will have opportunity to move touch and describe as well as discuss connections to their own life. Materials and Technologies/Resources/Pre Class Preparation: 22 objects in a bag Engage/Explore : 2 min 1. Show students mystery bag and ask students what they think is inside? “I have a mystery bag here that has 22 objects inside the bag. What do you think could be in the bag?” Explain: 2 min 1. Take out item and describe it compared to the one their partner has beside them. “You are going to take out an object, you are going to compare (say how it is like) the object beside you, or contrast (say how it is different), I want you to try using words that describe its size. What are some words that describe size” Provide Example 17
Extend: 10-12 min 1. Hand first student the bag and remind students to listen well. “I am going to hand (name) the bag to take out an object, I want all of you listening to people’s answers, they may use words that you haven’t thought of.” Exit/Evaluate: 5-8 min 1. Ask and discuss how students we can use comparing sizes and lengths in the world around us? “ I want you to turn to a partner and come up with a reason on why being able to compare sizes and lengths would help us or where we can see a use for this in the world around us?” Adaptations, Modifications & Extensions: Notes and Reflection: Gratitude and Future Hopes - students made great connections to the world - Maybe need to define shorter, longer, thinner, thicker, some students didn’t know what they meant. 18
Math: Compared to What? Learning Experience Number: 2 Length of Learning Experience: 25-35 min Curriculum Area: Math Curriculum Plan: Compare length and size Core Competencies Critical Thinking Question and Investigate I can experiment with different ways of measuring. Understand – Big Idea: EU1: Measurement helps me compare and identify different objects. EQ: What similarities and differences do I see in the size of things around me? What does this look like? Know/Do/Value Student will choose reasonably size objects to Develop and demonstrate an understanding measure, and will begin to proper sizing of object length and size through play inquiry. language. (C1, K2) Student Friendly Version of Intended Learning Standards/Curricular Competencies and Content: I can compare length and size of objects. Flexible Learning Context: Learning is holistic, reflexive, reflective, experiential and relational (focused on connectedness on reciprocal relationships and a sense of place). Students will be a part of group discussion, movement and exploring as well as partner work. Materials and Technologies/Resources/Pre Class Preparation: White boards 22 Markers 22 Partners chosen Explore : 10 min Notes or Modifications: 1. Students will walk around the classroom to find and bring an object to the carpet to share based on posed questions: Question #1: What can you find in the classroom that is about as long as your finger? “We are going to do a little exploring with size. I am going to give you a few questions and you are going to have to find objects the measure up. I do not want to see running, we are walking and observing what we could use to measure. You may bring the object to the carpet and share. The first question is find something in the classroom that is about as long as your finger?” 2. Questions #2: Smaller than your foot? 3. Questions #3: Longer than your hand? 4. Question #4: What strategies did you use to find an object? Can you explain the size of something without the ability to compare it? “By me giving you an object to measure up against I gave you baseline. A baseline is what we use to explain or compare against. For example, if I said, this pencil is longer than my foot. You would know without seeing the pencil the approximate size.” 19
Explain: 1 min 1. Explain to students that they will be doing a partner activity where they will be describing an object to their partner based on size. “We are going to do an activity where you will have to describe an object to your partner who cannot see the object. Your partner will draw the object on a whiteboard. Your goal is to get the accurate size of the objec
measurement from standard to non-standard all over the world. Whether students are aware of it yet or not, they use measurement in their classroom, at home, and when they are out on the playground. This unit will help students to become aware of ways they already engage in measuring and ways they can grow and develop in their skills. Students
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