Dear Parents and Caregivers, Thank you for the support you give your child in learning mathematics. We would like to share some information to help you better understand Arizona’s College and Career Ready Standards. This is one in our series of letters intended to help you understand the work your child brings home. We will highlight some new language and strategies we will use to build understanding, help children make sense of numbers, and know the common methods we learned in school. This letter is about decimals. End-­‐of-­‐year goals Students in fourth grade are introduced to decimals as another way to represent fractions with denominators of tenths or hundredths. They will focus on solving word problems involving tenths and hundredths by creating visual models of simple fractions and decimals. They will use the symbols <, >, or = to compare two decimals to the hundredths place, and justify their conclusions using visual models and explanations. Students may also make connections of decimals to metric measurement and money. Vocabulary Decimal number: A number written using base ten; a number containing a decimal point Decimal point: A dot separating the ones and tenths places in a decimal number Equivalent decimals: Two decimals that name the same amount Reading decimals When reading decimal names, it is important to distinguish between ten and tenth, and hundred and hundredth. Ten and hundred refer to the whole numbers greater than one (10 and 100), while tenth and hundredth refer to numbers less than one (.1 and .01). Students will practice reading and writing the equivalent forms for fractions and decimals that include tenths and hundredths. When reading decimals, say the word “and” when naming the decimal point. For example, 3.15 would be read as “three and fifteen hundredths.” One tenth = = .1 One hundredth= = .01 Two and one tenth 2 = 2.1 Three and seven hundredths= 3
= 3.07 Models for decimals Base ten models and number lines are two commonly used models for decimals. one whole (1) one-­‐tenth (0.1) one-­‐hundredth (0.01) This number line is divided into tenths. For example, to model the decimal .53 a student might create a base ten model using base ten pieces or by shading part of a whole. Mesa Public Schools/Grade 4/ Decimals/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014). A place value chart is another model that is helpful in correctly reading and comparing decimals. .53 is greater than .5, because fifty-­‐three hundredths has three more hundredths than fifty hundredths (or five tenths.) Increases by multiples of 10 Decreases by multiples of 10 Hundreds Tens Ones • Tenths Hundredths • 5 3 • 5 0 To determine whether a decimal is greater than (>), less than (<), or equal to (=) another decimal, a student could also use a number line and an understanding of decimal notation for fractions. Example: Is .32 greater than (>), less than (<), or equal to (=) .4? Justify your answer. Students can represent values such as .32 or on a number line. .32 is greater than (or ) and less than (or ). It is closer to so it would be placed on the number line near that value. Decimals are also used when writing measurements in the metric system. Below is a chart that shows the decimals that are associated with metric measurement. Metric System of Measurement Prefix and Meaning Length Liquid Capacity Mass kilo-­‐ 1000 kilometer (km) kiloliter (kL) kilogram (kg) hecto-­‐ 100 hectometer (hm) hectoliter (hL) hectogram (hg) deka-­‐ 10 dekameter (dam) dekaliter (daL) dekagram (dag) 1 meter (m) liter (L) gram (g) deci-­‐ 0.1 decimeter (dm) deciliter (dL) decigram (dg) centi-­‐ 0.01 centimeter (cm) centiliter (cL) centigram (cg) milli-­‐ 0.001 millimeter (mm) milliliter (mL) milligram (mg) Note: The most frequently used metric units are in bold. Our money system is also a good model for decimal notation. One dollar can be written $1.00, one dime can be written $0.10 and one penny can be written $0.01. How to help at home •
Help your student correctly read decimal numbers by using “and” when reading the decimal point. •
When using money, help your child see the connection between writing dollars and cents with decimals. ($1.23 is one whole, two tenths and 3 hundredths.) •
Watch this video about comparing decimals from LearnZillion. http://learnzillion.com/lessons/34-­‐compare-­‐and-­‐order-­‐simple-­‐decimals •
Remember, making mistakes is a part of learning. Mesa Public Schools/Grade 4/ Decimals/2013 Authorization to reprint or disseminate must be granted by Mesa Public Schools (February-­‐2014).