ʻaoʻao  o 9

Nā Ana Pili Helu - Papa 5

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Ke Ana

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Nā Hana Hoʻomākalakala a me ka Manaʻo Hōʻailona Helu 

Operations and Algebraic Thinking

Kākau a unuhi i nā haʻi pili helu

Write and interpret numerical expressions

(1.1)

5.OA.A.1

Hoʻohana i nā kahaapo, nā kahaapo kihikihi, a i ʻole nā kahaapo ʻēheu ma nā haʻi pilihelu a huli i nā haʻi e loaʻa ai kēia mau kaha.

Use parentheses, brackets, or braces in numerical expressions and evaluate expressions with these symbols.

5.OA.A.2

Kākau i nā haʻi maʻalahi e palapala ana i nā hoʻonohonoho helu/huli a loaʻa me nā helu, a unuhi i nā haʻi pilihelu/makemakika me ka huli ʻole iā lākou. He laʻana, hoʻopuka i ka hoʻonohonoho helu/huli a loaʻa “e hoʻohui i ka 8 a me ka 7, a laila e hoʻonui i ka ʻelua” pēnei: 2 x (8 + 7). Hoʻokūʻike i ka 3 x (18932 + 921) he pākolu i ka 18932 + 921, me ka hoʻomākalakala ʻole i ka huinanui a i ʻole i ka hualoaʻa.

Write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. For example, express the calculation “add 8 and 7, then multiply by 2″ as 2 × (8 + 7). Recognize that 3 × (18932 + 921) is three times as large as 18932 + 921, without having to calculate the indicated sum or product.

Kālailai i nā lauana a me nā pilina

Analyze patterns and relationships

(1.2)

5.OA.B.3

Hoʻopuka he ʻelua lauana helu e hoʻohana ana i ʻelua lula i kuhi ʻia. Hoʻomaopopo i ka pilina o nā paukū pili. Kaulua i nā paʻa helu o nā paukū pili o nā lauana ʻelua, a kākuhi i nā paʻa helu ma ka papa kuhikuhina. He laʻana, ke kuhi ʻia ka lula “E hoʻohui i ka 3” a me ka helu hoʻomaka he 0, a me ka lula i kuhi ʻia “E hoʻohui i ka 6” a me ka helu hoʻomaka he 0, hoʻopuka i nā paukū ma ke kaʻina, a ʻike i nā paukū o kekahi kaʻina he pālua o nā paukū pili ma ke kaʻina hou aku. Wehewehe i ke kumu o kēia hopena.

Generate two numerical patterns using two given rules. Identify apparent relationships between corresponding terms. Form ordered pairs consisting of corresponding terms from the two patterns, and graph the ordered pairs on a coordinate plane. For example, given the rule “Add 3″ and the starting number 0, and given the rule “Add 6″ and the starting number 0, generate terms in the resulting sequences, and observe that the terms in one sequence are twice the corresponding terms in the other sequence. Explain informally why this is so.

Nā Helu a me nā Hana Hoʻomākalakala ma ke Kumu Hoʻonui Pāʻumi 

Number and Operations in Base Ten

Maopopo ka ʻonaehana kūana helu

Understand the place value system.

(2.1)

5.NBT.A.1

Hoʻokūʻike i ke kikohoʻe ma ke kūana helu ʻekahi he pāʻumi i ke kūana helu ma kona ʻākau a he 1/10 o ke kūana helu ma kona hema i loko o ka helu kikohoʻe lehulehu.

Recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and 1/10 of what it represents in the place to its left.

5.NBT.A.2

Wehewehe i nā lauana o nā ʻole o ka hualoaʻa i ka hoʻonui ʻana i kekahi helu i ka pāʻumi, a wehewehe i nā lauana o ke kau ʻana i ke kekimala i ka hoʻonui ʻana a i ʻole i ka puʻunaue ʻana i ka pāʻumi. Hoʻohana i ka helu ʻiʻo pāhoʻonui e hōʻike i ka pāʻumi.

Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use positive integer exponents to denote powers of 10.

5.NBT.A.3

Heluhelu, kākau, a hoʻohālikelike i nā kekimala a i ka hapa kaukani. a. Heluhelu a kākau i nā kekimala a i ka hapa kaukani me ka hoʻohana ʻana i nā helu kumu hoʻonui pāʻumi, nā inoa helu, a me ka unuhi kūana, e laʻa, 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). e. Hoʻohālikelike i ʻelua mau kekimala a i ka hapa kaukani me ka nānā ʻana i nā kikohoʻe ma nā kūana helu pākahi a me ka hoʻohana ʻana i nā hōʻailona >, =, a < no ka palapala ʻana i ka hopena o ka hoʻokūkū ʻana.

Read, write, and compare decimals to thousandths. a. Read and write decimals to thousandths using base-ten numerals, number names, and expanded form, e.g., 347.392 = 3 × 100 + 4 × 10 + 7 × 1 + 3 × (1/10) + 9 × (1/100) + 2 × (1/1000). b. Compare two decimals to thousandths based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.

5.NBT.A.4

Hoʻohana i ka ʻapomanaʻo i ke kūana helu e kolikoli i nā kekimala i nā kūana like ʻole.

Use place value understanding to round decimals to any place.

Hana i nā hana hoʻomākalakala o nā helu piha kikohoʻe lehulehu a o nā kekimala a i ka hapa haneli.

Perform operations with multi-digit whole numbers and with decimals to hundredths.

(2.2)

5.NBT.B.5

Hoʻonui me ka mākaukau i nā helu piha kikohoʻe lehulehu me ka hoʻohana ʻana i ke kaʻina helu kūmau.

Fluently multiply multi-digit whole numbers using the standard algorithm.

5.NBT.B.6

Huli a loaʻa nā helupuka piha o nā helu kumu puʻunaue nona ʻehā kikohoʻe a emi iho a me nā helu komo nona ʻelua kikohoʻe, me ka hoʻohana ʻana i nā kaʻakālai i hoʻokumu ʻia ma ke kūana helu, nā ʻanopili hana hoʻomākalakala, a me/a i ʻole ka pilina o ka hoʻonui me ka puʻunaue. Kahakiʻi a wehewehe i ka hoʻomākalakala ʻana ma o nā haʻihelu, nā lau huinahā lōʻihi, a me/a i ʻole nā kūkohu ʻili.

Find whole-number quotients with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.

5.NBT.B.7

Hoʻohui, lawe, hoʻonui a puʻunaue i nā kekimala a i ka hapa haneli, me ka hoʻohana ʻana i nā kūkohu hana lima a i ʻole nā kiʻi a me nā kaʻakālai i hoʻokumu ʻia ma ke kūana helu, nā ʻanopili hana hoʻomākalakala, a me/a i ʻole ka pilina o ka hoʻohui me ka lawe; hoʻopili i ke kaʻakālai i ke kiʻina hana kākau a wehewehe i ka hoʻoholo ʻana i ka hana kūpono.

Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.

Nā Helu a me nā Hana Hoʻomākalakala: Nā Hakina 

Number and Operations: Fractions

Hoʻohana i nā hakina kaulike no ke kaʻakālai e hoʻohui a lawe i nā hakina.

Use equivalent fractions as a strategy to add and subtract fractions.

(3.1)

5.NF.A.1

Hoʻohui a lawe i nā hakina o nā mahele/kinopiha ʻokoʻa (me nā helu ʻōʻā/helu pili nō hoʻi) ma o ke kuapo ʻana i nā hakina i loaʻa me nā hakina kaulike e hoʻopuka i nā huinanui like a i ʻole i ke koena o nā hakina me nā mahele/kinopiha like. He laʻana, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (I ka hoʻolaulā ʻana, a/b + c/d = (ad + bc)/bd).

Add and subtract fractions with unlike denominators (including mixed numbers) by replacing given fractions with equivalent fractions in such a way as to produce an equivalent sum or difference of fractions with like denominators. For example, 2/3 + 5/4 = 8/12 + 15/12 = 23/12. (In general, a/b + c/d = (ad + bc)/bd.)

5.NF.A.2

Hoʻomākalakala i nā polopolema huaʻōlelo/moʻolelo nane o ka hoʻohui ʻana a me ka lawe ʻana i nā hakina e hoʻopili ana i ka piha holoʻokoʻa hoʻokahi, a i nā manawa nō hoʻi e ʻokoʻa ai nā mahele/kinopiha, e laʻa, ma o ka hoʻohana ʻana i nā kūkohu hakina ʻikemaka ʻia a i ʻole nā haʻihelu e kū ana no ka polopelema/nane pilihelu. Hoʻohana i nā hakina kaha ana a me ka noʻonoʻo helu no nā hakina e kolikoli naʻau a hōʻoia i ke kūpono o nā haʻina. He laʻana, e hoʻokūʻike i ka haʻina hewa o ka 2/5 + 1/2 = 3/7 ma ka hoʻomaopopo ʻana i ka 3/7 < 1/2.

Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators, e.g., by using visual fraction models or equations to represent the problem. Use benchmark fractions and number sense of fractions to estimate mentally and assess the reasonableness of answers. For example, recognize an incorrect result 2/5 + 1/2 = 3/7 by observing that 3/7 < 1/2.

Hoʻohana a hoʻoloa i nā mea i maopopo ʻē e pili i ka hoʻonui ʻana a i ka puʻunaue ʻana e hoʻonui a e puʻunaue i nā hakina.

Apply and extend previous understandings of multiplication and division to multiply and divide fractions.

(3.2)

5.NF.B.3

Unuhi i ka hakina he puʻunaue ʻia o ka hoʻohelu/kinohapa e ka mahele/kinopiha (a/b = a ÷ b). Hoʻomākalakala i nā polopelema huaʻōlelo/moʻolelo nane pili helu e pili i ka puʻunaue ʻana i nā helu piha e kuhi ana i nā haʻina he hakina a i ʻole helu ʻōʻā/helu pili, e laʻa, ma o nā kūkohu hakina ʻikemaka ʻia a i ʻole nā haʻihelu e hōʻike i ka polopelema/nane pilihelu. He laʻana, unuhi i ka 3/4 ʻo ia nō ka loaʻa o ka puʻunaue ʻana i ka 3 i ka 4, me ka hoʻomanaʻo ʻana i ka hualoaʻa o ka hoʻonui ʻana i ka 3/4 i ka 4 he 3 a i ka hoʻokaʻana ʻia ʻana o 3 mau piha holoʻokoʻa e 4 kānaka, loaʻa ka mahele kaulike i nā kānaka pākahi a pau a ʻo kona nui he 3/4. Inā makemake 9 mau kānaka e hoʻokaʻana i ke ʻeke laiki he 50 paona ma ka nānā ʻana i ke ana kaumaha, ʻehia paona laiki e pono ai kēlā me kēia kānaka? Ma waena o nā helu piha ʻehia ka haʻina?

Interpret a fraction as division of the numerator by the denominator (a/b = a ÷ b). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers, e.g., by using visual fraction models or equations to represent the problem. For example, interpret 3/4 as the result of dividing 3 by 4, noting that 3/4 multiplied by 4 equals 3 and that when 3 wholes are shared equally among 4 people each person has a share of size 3/4. If 9 people want to share a 50-pound sack of rice equally by weight, how many pounds of rice should each person get? Between what two whole numbers does your answer lie?

5.NF.B.4

Hoʻohana a hoʻoloa i ka ʻike kahua e pili i ka hoʻonui ʻana e hoʻonui i ka hakina a i ʻole ka helu piha i ka hakina. a. Unuhi i ka hualoaʻa o ke (a/b) x q ma nā mahele o ka hoʻomahele ʻia ʻana e q ma b mau mahele kaulike; a me ka manaʻo like, ma ka hopena o ke kaʻina o nā hana hoʻomākalakala a x q ÷ b. He laʻana, hoʻohana i ke kūkohu hakina ʻikemaka ʻia e hōʻike i ka (2/3) x 4 = 8/3, a haku i ka moʻolelo e pili i ia haʻihelu. E hana like no ka (2/3) × (4/5) = 8/15. (I ka hoʻolaulā ʻana, (a/b) × (c/d) = ac/bd.) e. Huli i ka ʻili o ka huinahā lōʻihi nona nā ana ʻaoʻao he hakina ma o ke kau ʻana i nā kile anakahi huinahā like o ke anakahi hakina kūpono e pili i ka lōʻihi o nā ʻaoʻao, a hōʻike i ka ʻili he like a like me ka hoʻonui ʻana i ka lōʻihi o ke ana ʻaoʻao. Hoʻonui i nā ana lōʻihi hakina e loaʻa ka ʻili o nā huinahā lōʻihi, a hōʻike i ka hualoaʻa hakina he ʻili huinahā lōʻihi.

Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction. a. Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b. For example, use a visual fraction model to show (2/3) × 4 = 8/3, and create a story context for this equation. Do the same with (2/3) × (4/5) = 8/15. (In general, (a/b) × (c/d) = ac/bd.) b. Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.

5.NF.B.5

Unuhi i ka hoʻonui ʻana ma ka pālakio (hoʻololi ʻana i ka nui) ma o: a. Ka hoʻokūkū ʻana i ka nui o ka hualoaʻa i ka nui o hoʻokahi helu hoʻonui/heluhana, me ka ʻole o ka hoʻonui ʻana. e. Ka wehewehe ʻana i ke kumu e ʻoi aku ai ka hualoaʻa ma mua o kekahi helu ke hoʻonui ʻia ia helu i ka hakina e ʻoi aku i ka 1 (me ka hoʻokamaʻāina ʻana i ka pilina o ka hoʻonui ʻana i nā helu piha e ʻoi aku i ka 1); ka wehewehe ʻana i ke kumu e emi mai ai ka hualoaʻa ma mua o kekahi helu ke hoʻonui ʻia ia helu i ka hakina e emi mai i ka 1; a me ka hoʻopili ʻana i ke kahua hana o ka hakina kaulike he a/b = (n×a)/(n×b) i ka hopena o ka hoʻonui ʻana i ke a/b i ka 1.

Interpret multiplication as scaling (resizing), by: a. Comparing the size of a product to the size of one factor on the basis of the size of the other factor, without performing the indicated multiplication. b. Explaining why multiplying a given number by a fraction greater than 1 results in a product greater than the given number (recognizing multiplication by whole numbers greater than 1 as a familiar case); explaining why multiplying a given number by a fraction less than 1 results in a product smaller than the given number; and relating the principle of fraction equivalence a/b = (n×a)/(n×b) to the effect of multiplying a/b by 1.

5.NF.B.6

Hoʻomākalakala i nā polopelema/nane pilihelu maoli o ka nohona e pili i ka hoʻonui ʻana i nā hakina a me nā helu ʻōʻā/helu pili, e laʻa, ma o ka hoʻohana i nā kūkohu hakina e ʻikemaka ʻia a i ʻole nā haʻihelu e hōʻike i ka polopelma/nane pilihelu.

Solve real world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.

5.NF.B.7

Hoʻohana a hoʻoloa i ka ʻike kahua o ka puʻunaue ʻana e puʻunaue i nā hakina anakahi i nā helu piha a i nā helu piha i nā hakina anakahi. (He manaʻo: Hiki i nā haumāna ke hoʻokumu i nā kaʻakālai e puʻunaue i nā hakina me ka laulā inā hiki iā lākou ke hoʻonui i nā hakina me ka laulā, ma o ka hoʻoholo ʻana i ka pilina o ka hoʻonui a me ka puʻunaue. Akā ʻaʻole he koina ka puʻunaue ʻana i ka hakina i ka hakina ma kēia pae papa.) a. Unuhi i ka puʻunaue ʻana i ka hakina anakahi i ka helu piha non-zero, a hoʻomākalakala i ia ʻano helupuka. He laʻana, e haku i ka moʻolelo no (1/3) ÷ 4, a hoʻohana i ke kūkohu hakina i ʻikemaka ʻia e hōʻike i ka helupuka. Hoʻohana i ka pilina o ka hoʻonui a me ka puʻunaue e wehewehe i ka (1/3) ÷ 4 = 1/12 no ka mea (1/12) × 4 = 1/3. e. Unuhi i ka puʻunaue ʻana i ka helu piha i ka hakina anakahi, a hoʻomākalakala i ia ʻano helupuka. He laʻana, haku i ka moʻolelo no ka 4 ÷ (1/5), a hoʻohana i ke kūkohu hakina i ʻikemaka ʻia e hōʻike i ka helupuka. Hoʻohana i ka pilina o ka hoʻonui i ka puʻunaue e wehewehe i ka 4 ÷ (1/5) = 20 no ka mea 20 × (1/5) = 4. i. Hoʻomākalakala i nā polopelema/nane pilihelu maoli o ka nohona e pili i ka puʻunaue ʻana i nā hakina anakahi i nā helu piha non-zero a i ka puʻunaue ʻana i nā helu piha i ka hakina anakahi, e laʻa, ma o ka hoʻohana i nā kūkohu hakina i ʻikemaka ʻia a me nā haʻihelu e hōʻike i ka polopelema/nane pilihelu. He laʻana, ʻehia paona kokoleka a kēlā kānaka kēia kānaka inā hoʻokaʻana 3 kānaka i ka 1/2 paona kokoleka? ʻEhia kīʻaha 1/3 o 2 kīʻaha hua waina māloʻo?

Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions. (Note: Students able to multiply fractions in general can develop strategies to divide fractions in general, by reasoning about the relationship between multiplication and division. But division of a fraction by a fraction is not a requirement at this grade.) a. Interpret division of a unit fraction by a non-zero whole number, and compute such quotients. For example, create a story context for (1/3) ÷ 4, and use a visual fraction model to show the quotient. Use the relationship between multiplication & division to explain that (1/3) ÷ 4 = 1/12 because (1/12) × 4 = 1/3. b. Interpret division of a whole number by a unit fraction, and compute such quotients. For example, create a story context for 4 ÷ (1/5), and use a visual fraction model to show the quotient. Use the relationship between multiplication and division to explain that 4 ÷ (1/5) = 20 because 20 × (1/5) = 4. c. Solve real world problems involving division of unit fractions by non-zero whole numbers and division of whole numbers by unit fractions, e.g., by using visual fraction models and equations to represent the problem. For example, how much chocolate will each person get if 3 people share 1/2 lb of chocolate equally? How many 1/3-cup servings are in 2 cups of raisins?

Ke Ana ʻAna a me ka ʻIkepili/ʻIke 

Measurement and Data

Hoʻohulihuli i nā anakahi like o ka ʻonaehana ana i kuhi ʻia.

Convert like measurement units within a given measurement system.

(4.1)

5.MD.A.1

Hoʻohulihuli i nā anakahi ana kūmau ma loko o kekahi ʻōnaehana ana (e laʻa, e hoʻohulihuli i ka 5 knm i ka 0.05 m), a hoʻohana i kēia hoʻohulihuli ʻana ma ka hoʻomākalakala ʻana i nā polopelema e pono ana he mau kaʻina hana.

Convert among different-sized standard measurement units within a given measurement system (e.g., convert 5 cm to 0.05 m), and use these conversions in solving multistep real world problems.

Hōʻike i ke kū ʻana a wehewehe i ka ʻike/ʻikepili.

Represent and interpret data.

(4.2)

5.MD.B.2

Kaha i ka laina pakuhi e hōʻike i ke kaina/pūʻulu ʻikepili/ʻike o nā ana ma nā hakina o kekahi anakahi (1/2, 1/4, 1/8). Hoʻohana i nā hana hoʻomākalakala i nā hakina no kēia pae papa e hoʻomākalakala i nā polopelema/nane pilihelu e pili ana i ka ʻike ma nā laina pakuhi. He laʻana, i ka ʻike ʻana i nā ana wai like ʻole ma nā kānuku like loa, e huli i ka nui wai o kēlā kānuku kēia kānuku inā hoʻokaʻana hou ʻia ka wai ma waena o nā kānuku.

Make a line plot to display a data set of measurements in fractions of a unit (1/2, 1/4, 1/8). Use operations on fractions for this grade to solve problems involving information presented in line plots. For example, given different measurements of liquid in identical beakers, find the amount of liquid each beaker would contain if the total amount in all the beakers were redistributed equally.

Ke Ana Anahonua - maopopo nā manaʻo o nā huina a ana i nā huina 

Geometric measurement–understand concepts of angle and measure angles.

(4.3)

5.MD.C.3

Hoʻokūʻike i ka pīhanahaka he hiʻohiʻona o nā kinona paʻa a maopopo nā manaʻo no ke ana ʻana i ka pihanahaka. a. “Hoʻokahi paʻaʻiliono anakahi” ka pihanahaka o ka paʻaʻiliono nona ka ʻaoʻao he 1 anakahi o kona lōʻihi, a hiki ke hoʻohana ʻia ʻo ia no ke ana ʻana i ka pihanahaka. e. Inā hiki ke hoʻopiha ʻia kekahi kinona paʻa me ka hakahaka ʻole a i ʻole ka ʻiliʻili ʻole e n mau paʻaʻiliono anakahi, he n paʻaʻiliono anakahi pāhoʻonui ʻekolu kona pihanahaka.

Recognize volume as an attribute of solid figures and understand concepts of volume measurement. a. A cube with side length 1 unit, called a “unit cube,” is said to have “one cubic unit” of volume, and can be used to measure volume. b. A solid figure which can be packed without gaps or overlaps using n unit cubes is said to have a volume of n cubic units.

5.MD.C.4

Ana i ka pihanahaka ma o ka helu ʻana i nā paʻaʻiliono anakahi, me ka hoʻohana ʻana i nā kenimika pāhoʻonui ʻekolu, i nā ʻīniha pāhoʻonui ʻekolu, a me nā anakahi e loaʻa.

Measure volumes by counting unit cubes, using cubic cm, cubic in, cubic ft, and improvised units.

5.MD.C.5

Hoʻopili i ka pihanahaka i nā hana hoʻomākalakala ʻo ka hoʻonui a me ka hoʻohui a laila hoʻomākalakala i nā polopelema/nane pilihelu maoli o ka nohona a me nā polopelema/nane pilihelu e pili i ka pihanahaka. a. Huli i ka pihanahaka o ka ʻōpaka huinahā lōʻihi kūpono nona nā ana lōʻihi helu piha o nā ʻaoʻao ma o ka hoʻopiha ʻana iā iā i nā paʻaʻiliono anakahi, a hōʻike i ka pihanahaka he like a like me ka hoʻonui ʻana i nā lōʻihi o kona mau kaʻe, a pēlā pū me ka hoʻonui i kona ʻili i kona kiʻekiʻe. Hōʻike i ka hualoaʻa he helu piha pākolu no ka pihanahaka, e laʻa, e hōʻike i ke ʻanopili hoʻolike o ka hoʻonui ʻana. e. Hoʻohana i ka haʻilula P = l x a a me P = kahua x kiʻekiʻe no ka huli ʻana i nā pihanahaka o nā ʻōpaka huinahā lōʻihi kūpono nona nā lōʻihi helu piha o nā kaʻe ma ka hoʻomākalakala ʻana i nā polopelema/nane pilihelu maoli o ka nohona a me nā polopelema makemakika/nane pilihelu. i. Hoʻokūʻike i ka pihanahaka he mea hoʻohui. Huli i ka pihanahaka o nā kinona paʻa nona ʻelua ʻōpaka huinahā lōʻihi kūpono e ʻiliʻili ʻole ma o ka hoʻohui ʻana i nā pihanahaka o nā mahele ʻiliʻili ʻole, a me ka hoʻohana ʻana i kēia kiʻina hana e hoʻomākalakala i nā polopelema/nane pilihelu maoli o ka nohona.

Relate volume to the operations of multiplication and addition and solve real world and mathematical problems involving volume. a. Find the volume of a right rectangular prism with wholenumber side lengths by packing it with unit cubes, and show that the volume is the same as would be found by multiplying the edge lengths, equivalently by multiplying the height by the area of the base. Represent threefold wholenumber products as volumes, e.g., to represent the associative property of multiplication. b. Apply the formulas V = l × w × h and V = b × h for rectangular prisms to find volumes of right rectangular prisms with whole-number edge lengths in the context of solving real world and mathematical problems. c. Recognize volume as additive. Find volumes of solid figures composed of two nonoverlapping right rectangular prisms by adding the volumes of the non-overlapping parts, applying this technique to solve real world problems.

Ke Anahonua 

Geometry

Kākuhi i nā kiko ma ka papa kuhikuhina e hoʻomākalakala i nā polopelema/nane pilihelu maoli o ka nohona a o ka makemakika/pilihelu

Graph points on the coordinate plane to solve real-world and mathematical problems.

(5.1)

5.G.A.1

Hoʻohana i ka paʻa laina kūpono, kapa ʻia he mau iho, e wehewehe i ka ʻōnaehana kuhikuhina, me ka hui ʻana o nā laina (ke kumu piko) e hoʻonohonoho ʻia ma ka 0 ma nā laina pākahi a kuhi ʻia ke kiko ma ia papa kuhikuhina e hiki ke huli ʻia ma o ka paʻa helu kuhikuhina, kapa ʻia kona kuhikuhina. Maopopo ka helu mua ke kaʻawale ona mai ke kumu piko ma kekahi iho, a ʻo ka helu ʻelua ke kaʻawale ona ma ka iho hou aku, me ka hana maʻamau e pili nā inoa o nā iho ʻelua me ke kuhikuhina (e laʻa, ka iho-x a me ke kuhikuhina-x, ka iho-y a me ke kuhikuhina-y).

Use a pair of perpendicular number lines, called axes, to define a coordinate system, with the intersection of the lines (the origin) arranged to coincide with the 0 on each line and a given point in the plane located by using an ordered pair of numbers, called its coordinates. Understand that the first number indicates how far to travel from the origin in the direction of one axis, and the second number indicates how far to travel in the direction of the second axis, with the convention that the names of the two axes and the coordinates correspond (e.g., x-axis and x-coordinate, y-axis and y-coordinate).

5.G.A.2

Hōʻike i nā polopelema/nane pilihelu maoli o ka nohona a me nā polopelema makemakika/nane pilihelu ma o ke kākuhi ʻana i nā kiko ma ka ‘āpana hapahā mua o ka papa kuhikuhina, a unuhi i ka waiwai kuhikuhina o nā kiko e pili i ke kahua.

Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.

Waeʻano i nā kinona papa ma nā mahele o ko lākou hiʻohiʻona.

Classify two-dimensional figures into categories based on their properties.

(5.2)

5.G.B.3

Maopopo ke komo ʻana o nā hiʻohiʻona o kekahi mahele (i waeleʻa ʻia) o nā kinona papa ma nā mahele liʻiliʻi a pau o ia mahele. He laʻana, ʻehā huina o nā huinahā lōʻihi a pau, a he huinahā lōʻihi ka huinahā like, no laila ʻehā huina o ka huinahā like.

Understand that attributes belonging to a category of twodimensional figures also belong to all subcategories of that category. For example, all rectangles have four right angles and squares are rectangles, so all squares have four right angles

5.G.B.4

Waeleʻa i nā kinona papa ma ke kau kūlana ʻana ma o nā hiʻohiʻona.

Classify two-dimensional figures in a hierarchy based on properties.

Nā Ana Kā Mua - Papa 5 Pili Helu

K. Akioka

Nowemapa 2013