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Math-4-Parents Fall Workshops K-4 Central School Tammy Fisch, Math teacher October 2014 • Discuss math content, language, and teaching methods that are being used in classrooms today • Increase understanding of why our children are learning various strategies • Explore hands-on math activities using manipulatives • Discuss games and activities to do at home to support mathematical thinking Kindergarten Overview • Know number names and count to tell numbers of objects. • Compare groups of objects, up to 10 • Fluently add and subtract within 5 • Add within 10 using objects or drawings • Decompose numbers to 10 into pairs in more than one way 1st Grade Overview • Developing understand of addition and subtraction, and strategies for addition and subtraction within 20 • Developing understanding of whole number relationships and place value, including grouping tens and ones • Developing understanding of linear measurement and measuring lengths as iterating length units • Reasoning about attributes of, and composing and decomposing geometric shapes Daily Routines: Building Number Sense • Count days of school: 10 frames, place value bundles • Calendar • Quick Images, Rekenreks Represent numbers flexibly Some students may know that this frame has 5! 5 6, 7, 8 Number Bonds • Number bonds help students see that numbers can be "broken" into pieces to make computation easier. • Children experience multiple ways to decompose the same number, rather than memorizing. • The part/part/whole mat and concrete practice are used a LOT! This helps little ones really understand how addition and subtraction are related. •Students can find combinations in a systematic way by sliding one bead at a time from one side to the other. •Notice the part/part/total relationship shown on the bracelet. •Students should verbalize each combination (0 and 3 make 3, 1 and 2 make 3, etc.). The Power of 10 • 1st graders begin learning their basic addition facts and apply that knowledge in a strategy known as "make a ten”. • This helps make sense of facts that might otherwise be hard to memorize, such as 8 + 4 or 9 + 5. • Students decompose one of the addends to make a ten from the other. In the example pictured below, the 4 is decomposed (split) into 3 and 1. The 3 is combined with the 7 to make 10, and then the 1 is added for 11. Understanding the Problems •What is happening in the story? •Can you tell the story without numbers? •Visualize/act out the story. •Draw or use manipulatives to show what is happening. Part-Part-Total Models Kate and Nana baked some cookies. They made 2 heart cookies and some square cookies. They baked 8 cookies altogether. How many square cookies did they bake? There are 8 juice boxes on the table. Some children drank their juice. Now there are only 5 juice boxes. How many juice boxes were taken from the table? Let’s take a peek! nd 2 Grade Overview • Extending understanding of base-ten (place value) • Building fluency with addition and subtraction • Using standard units of measure • Describing and analyzing shapes Developing Place Value Understanding Students practice counting & creating “bundles” and then represent numbers in expanded form. Stages of Representation 100 + 100 + 10 + 10 + 10 + 1 + 1 + 1 = 243 200 + 30 + 3 = 243 Concrete - Pictorial - Abstract Read-Draw-Write 399 jars of baby food are sitting on the shelf at the market. Some jars fall off and break. 389 jars are still on the shelf. How many jars broke? Concrete - Pictorial - Abstract 1. 2. Ben and his dad have sold 60 chocolate chip cookies at the school bake sale. If they baked 100 cookies, how many cookies do they still need to sell? Samantha is helping the teacher organize the pencils in her classroom for the teacher. She finds 41 yellow pencils and 29 blue pencils. She threw away 12 that were too short. How many pencils are left in all? Lisa solves 166 – 48 vertically on her place value chart. Explain what Lisa did correctly and what she needs to fix. The correct answer is not enough. How you get the answer matters, too! Hundreds 100’s Tens 10’s Ones 1’s Use math drawings to represent additions with up to two compositions and relate drawings to a written method. As students write addition problems vertically and make math drawings, they are reminded to be precise in aligning the digits and in drawing their dots in neat 5-groups. 3rd Grade Overview • Developing understanding of multiplication and division and strategies for multiplication and division within 100 • Developing understanding of the structure of rectangular arrays and of area • Developing understanding of fractions • Describing and analyzing two-dimensional shapes Tape Diagrams or Bar Models The use of the rectangular bars and the identification of the unknown quantity with a question mark help students visualize the problem and know what operations to perform— in short, viewing all problems from an algebraic perspective beginning in early elementary grade levels. ―drawing a picture‖ usually this entails drawing objects, animals, or counters. It is not very efficient when you move to larger numbers. When you use bar modeling, students learn to represent these objects with rectangles that enable them to see the number relationships, rather than focusing on the objects of the problems. Rectangles are used because they are easy to draw, divide, represent larger numbers, and display proportional relationships. There are 21 fish in a bowl. Fifteen are from a student. The rest are from the school. How many are from the school. Grant buys 345 fruit bars. Ken buys 230 more fruit bars than Grant. How many fruit bars does Ken buy? Read-Draw-Write Red, orange, and blue scarves are on sale for $4 each. Nina buys 2 scarves of each color. She also buys a hat that costs $4. How much does she spend altogether? Arrays 7 x 5 = ( 5 x 4 ) + ( 5 x 3 ) 35 = 20 + 15 2x4=4x2 4+4=2+2+2+2 Commutative Property of Multiplication states that changing the order of factors does not change the product. Four groups of 2 is the same as two groups of 4, but one is more efficient. Students begin to apply this property when solving multiplication problems. Distributive Property of Multiplication states that the product of a number is equal to the sum of the individual products and the number. I can use the distributive property to solve multiplication problems I don’t know more efficiently. 8x8=? (8 x 4) + (8 x 4) = ? 32 + 32 = 64 Number Bonds 4 sixes 2 sixes 2 sixes 2 sixes + 2 sixes = 4 sixes 4x6 4 groups of 6 4x6 2x6 2x6 ( 2 x 6 ) + ( 2 x 6 ) = 24 Area of Figures The tile floor in Brandon’s living room has a rug on it as shown below. How many square tiles are on the floor, including the tiles under the rug? th 4 Grade Overview (1) Developing understanding and fluency with multi-digit multiplication, and developing understanding of dividing to find quotients involving multi-digit dividends; (2) Developing an understanding of fraction equivalence, addition and subtraction of fractions with like denominators, and multiplication of fractions by whole numbers; (3) Understanding that geometric figures can be analyzed and classified based on their properties, such as having parallel sides, perpendicular sides, particular angle measures, and symmetry. Word Problems & Tape Diagrams Jennifer texted 5,849 times in January. In February , she texted 1,263 more times than she did in January. What was the total number of text messages that Jennifer sent in the two months combined? Explain how you would check the reasonableness of your answer. X and ÷ by 10 A rectangle is 1 inch wide. It is 3 times as long as it is wide. Use square tiles to find its length. 1‖ 1‖ 1‖ 1‖ “ ___ times as many” The basketball team is selling t-shirts for $9 each. On Monday, they sell 4 tshirts. On Tuesday, they sell 5 times as many t-shirts as on Monday. How much money did the team earn altogether on Monday and Tuesday? Multiplication Models •Students learn to decompose numbers into base ten units in order to find products of single-digit by multi-digit numbers. •Students use the distributive property and multiply using number disks to model. •Students bridge partial products to the recording of multiplication via the standard algorithm. Division Models • Students represent division with single-digit divisors using arrays and the area model, followed by the place value disks. • The standard division algorithm is taught using students’ knowledge of place value, decomposing unit by unit. Why Does the Algorithm Work? Emma takes 57 stickers from her collection and divides them up equally between 4 of her friends. How many stickers will each friend receive? Emma puts the remaining stickers back in her collection. How many stickers will Emma return to her collection? Algorithm – step by step Providing Support at Home • Supporting work habits instead of work – – – – What is the question asking? What information do we need to solve? What is a reasonable answer? Why? What steps do we need in order to solve the problem? • Don’t provide too much support. Homework is an important assessment tool for the teacher. • Provide tools to help your child solve problems. • Focus more on the why and how than simply getting the correct answer. How can we bring math into our children’s worlds? • • • • • • • Count everything! Play games Talk about math Talk about our thinking Explain why something works Explore new ideas and make generalizations Take a risk, It’s OK to make a mistake and struggle! It’s the questions that drive mathematics. • Encourage them to explain their thinking. • By expressing wonder and amazement at what they are figuring out! • “Can you show me how you got that answer?” • • • • “How do you know? Can you show me?” “Interesting, can you prove it?” “Do you think it will always work?” “What do you think it would look like if we put it on paper?” Educate Yourself Math Module Parent Letters Play, Play , Play! Math Resources Central School homepage Support Services Math AIS Your feedback is important