Questions On Rational Number Assessment

It is crucial to develop in children the ability to tackle problems with initiative and confidence…mathematics has changed from careful rehearsal of standard procedures to a focus on mathematical thinking and communication to prepare them for the world of tomorrow (Anghileri, 2006, p.2).

The aims and importance of learning provision for numeracy development are to ensure all students understand that maths is a vital part of everyday life and will continue to be used throughout their life. Primary schools will teach students to learn various methods and techniques to be able to reach the correct answer. The end goal means more students will be able to solve a mathematical problem, independently, using a method that suits them. They can then develop their learning to improve their knowledge and apply it to real life situations; such as counting in groups of numbers such as 5’s or 10’s, which in turn can be applied when paying for

Through the Rational Number Interview I was able to gain insight into Adams mathematical understanding of fractions, decimals and percentages. As a student in year 5, Adam was able to make connections using various mathematical strategies. Adam has an understanding of infinite numbers, for example, when asked how many decimals are there between each rational number (0.1 and 0.11), he answered promptly with “many numbers”. Adam was able to acknowledge that a fraction can be shown as a division problem, “divide the pizza into fifths and each get 3 pieces”. He was able to calculate by partitioning the pizza, and by dividing each pizza into the amount of people (5). Adam shows residual thinking when building up to the whole

Students will use the words more or greater than, less than, same or equal to through and interactive text on numbers.

Today we will be learning about place value. When we divide numbers with three and four digits by a one digit number, the quotient doesn’t always go about the first number in the dividend like we saw yesterday. This is important to know because if you had to split $100 with your sister and you divided $100 by 2 and placed the 5 above the 1, then added two zeros, you would have to pay your sister $500. That’s not dividing, or fair. Remember we need to know how to divide so you can evenly split something, like money.”

| 11. Is the sequence 5, 9, 15, ... an arithmetic sequence? Explain. Type your answer below.

He can convert improper fractions to a mixed number with 57% accuracy and convert mixed numbers to improper fractions with 80% accuracy. John can simplify a fraction with 92% accuracy. However, he does not always simplify his answer, instead he stops with his answer rather than seeing if it can be simplified. He can add and subtract fractions with 88% accuracy. He can multiply a fraction by a fraction with 14% accuracy and by a whole number with 90% accuracy. He can divide a fraction by a whole number and a whole number by a fraction with 89% accuracy. He needs to be able to simplify fractions when computing with fractions. He needs to be able to add, subtract, multiply, and divide fractions. He needs to identify the correct operation to solve a word problem. He needs to be able to solve one-step and multi-step word problems involving all 4 operations (addition, subtraction, multiplication, and division) of whole numbers and fractions. John’s weaknesses in math impact his ability to solve multi-step word problems, which is expected in 5th

Teachers play an important role in fostering mathematics skills. In the “play dough” (Appendix A) episode, the educators can push student thinking and place the burden of thought on the student. Strategic questioning can really promote higher order thinking a natural integration between math and play (National Council of Teachers of Mathematics [NCTM], 1999). Questions such as “How can you tell which one is the biggest/smallest? How do you put them in order? Teachers should be encouraged to think about, not only the questions they are asking as children are working but also the frame that sets students off to larger problem solving and mathematical discoveries – measure and compare the lengths and capacities (ACARA, 2016). It is important for teachers to think about the questions that are embedded in the task itself but must also analyse the questions to ensure that children are set on a path to deeper understanding of the concept being taught rather than rote regurgitation – as evident in the play dough experience chosen. When it comes to questioning, educators “need to know when to probe, when to wait for answers and when to reinforce responses and when not ta ask questions” (NCTM, 1999, p.187). As seen in the ‘play dough’ (Appendix A) activity chosen, educators can introduce the mathematical concept of measurement and connect new knowledge with old through the use of effective questioning which crates a “link between actions and the language” (Knaus, 2013,

Similarly, the Jordan study proved a direct link between counting and focusing on strengthening number sense and increased reasoning and mathematical understanding across different forms of assessment. Most notably, the number sense group my strong and sustainable gains on story problems,

Understanding place value is integral to mathematics, and is especially for addition and subtraction. Being able to easily rearrange numbers between place values is required for most addition and subtraction problems. Part of grasping place value is being able to unitize. Fosnot and Dolk explain unitizing to be “a child’s construction of the logic to think of 10 flexibly as ten 1’s or as one unit of 10” (Taylor, Breck, & Aljets, 2004, p. 140). Unitizing is what makes “borrowing” in subtraction possible. If a problem is 32 – 16, one of the three tens must be broken up into units in order to subtract; being able to see 32 as 3 tens and 2 ones and as 2 tens and 12 ones is what makes the problem possible. Place value and unitizing have much to do with a comprehension of base ten, but they are not exclusive to base ten. For example, one could apply the idea of place value and unitizing to base five. The number 18510 would be written as 12205. The place values would then be 125, 25, 5, and 1 (instead of 1000, 100, 10, and 1), and 12205 would be understood as one 125, two 25s, and two 5s. Unitizing would allow for someone to

It is important to teach children numeracy to suit their age and use appropriate techniques to suit their age and ability because sometimes too much emphasis on formal recording of 'sum' if introduced to early to children could make it difficult for them to understand. The learning style of numeracy is given more emphasis today to make them understand it much better. In the early years emphasis is made on how to make children understand different methods of working out to be able to arrive to an answer. Working with children the aim is to give children solid ground on

This week I was observed during a particularly challenging math lesson. My lesson was elapsed time. My hope was to successfully try Sherry Parish’s, Number Talks method that Sabine Smead at Boulder County School for Integrated Studies, had introduced and modeled for us the week before at Friday Seminar.

It is important for musicians to understand the relationships and values of fractions in order to correctly hold a note.”

Multiplicative thinking, fractions and decimals are important aspects of mathematics required for a deep conceptual understanding. The following portfolio will discuss the key ideas of each and the strategies to enable positive teaching. It will highlight certain difficulties and misconceptions that children face and discuss resources and activities to help alleviate these. It will also acknowledge the connections between the areas of mathematics and discuss the need for succinct teaching instead of an isolated approach.

Multiplication by ten gives students opportunity to explore larger numbers, and can also be extended on(Reys et al. ch. 11.4). In addition, multiples of 10 give students the knowledge that all digits move left one place and an additional place hundreths. This concept can be used to introduce the decimal place which is also moving place each time something is multiplied by tens. Exposing students to a range of examples which displays patterns that occur when multiplying by tens and hundreths will generate meaning of digits moving place (Reys et al., ch. 11.4).