كتاب دليل المعلم الرياضيات Reveal الصف السابع منهج انجليزي الفصل الثالث 2021 2022

**Standards for Mathematical Practice**

Make sense of problems and persevere in solving them

Mathematically proficient students start by explaining to themselves the meaning of a problem and for entry to its sdution

They analyze givens, constraints, relationships , and goals. They make cmjectures about the form and meaning of the solution and plan a sd ution pathway rather than simply jumping into a solution attempt They consider proWems, and try cases and simpl er forms of the original cyoblem in order to gain insight into its solution They monitor evaluate their ami change course if necessary . Older students might. dgmding on the context of the problem , transform algebraic expressions or the viewing window on their graphing calculator to the information they need

Mathematically proficient students can explain equations. verbal descriptims. tables . and graphs or draw cfiagrams of features and relatimships , graph data. and sea rch for regularity trends. Younger students might rely on using concrete objects to help conceptualize and save a problem. Mathematically proficient students check their answers to problems using a different method. and they continually ask themselves. "DIE this make sense ? " They can understand the apcymches of others to solving complex problems and identity correscmdences between different approaches

Reason abstractly quantitatively Mathematica Ily proficient students make sense of quantities and their relationships in problem situations. They bring two complementary abil ities to bear on proNems involving quantitative relatimships the ability to decontextualize — to abstract a given situation and represent it symbolically and manipulate the representing symbols as if they have a life of their own. without necessarily attendng to their referents — and the ability to contextualize. to pause asneeded during the manipulation process in order to probe into the referents for the symbols involved. Quantitative reasoning entails habits of creating a representation of the problem at hand: considering the units involved: attencfing to the meaning of quantities , not just how to compute them ; and knowing and flexibly using different gyoperties of and objects

**Standards for Mathematical Practice**

Construct viable arguments and critique the reasming of others

Mathematically proficient students understand and use stated assumptions. defritions , and previously established results in constructing arguments. They make conjectures and build a cal progression of statements to explore the truth of their conjectures

They are a ble to analyze situations by breaking them into cases , and can recognize and use counterexamples. They justify their conclusions, communicate them to others , and reswld to the arguments of others. They reason inductively atmJt data, making plausible arguments that take into accomt the context from which the data arose. Mathematically proficient students are also able to compare the effectiveness of two plausible arguments. distinguish correct logic or reasoning from that which is flawed, and—if there is a flaw in an argument—explain what it is. Elementary students can construct arguments using concrete referents such as objects , drawings, diagrams , and actions. Such arguments can make sense and be correct, even though they are not generalized or made formal unu later grades. Later. students learn to determine domains to which an argument applies. at all grades can listen read the arguments of others, decide whether they make sense, and ask

useful questions to darify or improve the arguments

**with** **nuttpmatics**

Mathematically proficient students can apply the mathematics they know to solve problems arising in everyday life. society. and the workplace. In early grades. this might be as simple as writing an ad&tion equabon to a situation. In middle grades, a student might apply proportional reasoning to plan a school event or analyze a in the community. By high school, a student might use geometry to solve a design problem or use a function to describe how one quantity of interest depends on another. Mathematically proficient students who can apply what they know a re making assumptions and approximations to simplify a conWicated situation , realizing that these may need revision later. They are able to identity quantities in a situation and map their relationships using such tools as diagrams. two-way tables. graphs, flowcharts and formulas. They can analyze those relationships mathematically to draw conclusions. They routinely interpret their mathematical results in the context of the situation and reflect on M whether the results make sense- imorovina the model if

**Standards for Mathematical Practice**

Use appropriate tools strategically Mathematica Ily proficient students consider the available tods when saving a mathematical problem. These might include cmcil and paper. concrete a ruler. a protractor. a calculator a spreadsheet. a computer system. a statistical or dynamic geometry software. Prffcient are sufficiently familiar with appropriate for their grade or cmrse to make sound cmsims about when each of these tcxls might be helpful bcth the insight to be gained and their limitations. For example. mathematically proficient high sctml students analyze graphs of functions and sol utions using a graphing calculator. They detect possble errors by strategically using estimation and other mathematical When making mathematical models. they know that can enable them to visualize the results of varying assumptions. explore consequences. and compare predictions with data. Mathematically proficient students at various grade levels are able to identify relevant external mathematical resources , such as digital content lcxated on a website. and use them to pose or seve probems. They are able to use technological tnls to explore and deepen their of concepts

**Attend to precision**

Mathematically proficient students try to communicate precisely to others. They try to use dear definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. including using the equal sign consistently and appropriatety They are careful about units of measure. and latkling axes to clarify the correspondence with quantities in a problem calculate accurately and efficiently , express numerical answers with a degee of precision appropriate for the problem context In the elementary grades, students give carefully formulated explanations to each other . By the time they reach high they have learned to examine claims and make explicit use of definitions