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In this article the authors describe a project during which they unpacked fraction standards, created rigorous tasks and lesson plans, and developed formative and summative assessments to analyze students' thinking about fraction multiplication. The purpose of this article is to (1) illustrate a process that can be replicated by educators interested in using rigorous mathematical tasks and assessments to support and advance their students' mathematical thinking; and (2) share the artifacts and instructional products that educators can use to improve mathematics assessment practices.

Cerebral magnetic resonance imaging was undertaken, at 3 Tesla field strength, employing magnetization transfer (MT) and diffusion-weighted imaging (DWI) sequences, in 26 patients with well-compensated cirrhosis, free of overt hepatic encephalopathy. Results were compared to those from 18 aged-matched healthy volunteers. Cerebral magnetization transfer ratios (MTR) were reduced in the frontal white matter, caudate, putamen and globus pallidus in patients with cirrhosis, compared to healthy controls, while the apparent diffusion coefficients (ADC) on DWI were significantly increased in the genu and body of the corpus callosum. An association between previous excessive alcohol consumption and both MTR and ADCs was noted, but this association was lost when controls were exercised for the severity of liver disease and psychometric impairment on multivariate analysis. Eight (31 %) of the 26 patients had impaired psychometric performance consistent with a diagnosis of minimal hepatic encephalopathy. No statistically significant difference in regional cerebral MTRs or ADCs was found in relation to neuropsychiatric status, although there was a trend towards lower MTRs in patients with impaired psychometric performance. The alterations in MTR and ADC in the patients with functionally compensated cirrhosis are compatible with theories governing the genesis of hepatic encephalopathy, including changes in astrocyte membrane permeability, with subsequent redistribution of macromolecules.

The presence of overt hepatic encephalopathy (HE) is associated with structural, metabolic and functional changes in the brain discernible by use of a variety of magnetic resonance (MR) techniques. The changes in patients with minimal HE are less well documented. Twenty-two patients with well-compensated cirrhosis, seven of whom had minimal HE, were examined with cerebral 3 Tesla MR techniques, including T 1 - and T 2 -weighted, magnetization transfer and diffusion-weighted imaging and proton magnetic resonance spectroscopy sequences. Studies were repeated after a 4-week course of oral L-ornithine L-aspartate (LOLA). Results were compared with data obtained from 22 aged-matched healthy controls. There was no difference in mean total brain volume between patients and controls at baseline. Mean cerebral magnetization transfer ratios were significantly reduced in the globus pallidus and thalamus in the patients with cirrhosis irrespective of neuropsychiatric status; the mean ratio was significantly reduced in the frontal white matter in patients with minimal HE compared with healthy controls but not when compared with their unimpaired counterparts. There were no significant differences in either the median apparent diffusion coefficients or the mean fractional anisotropy, calculated from the diffusion-weighted imaging, or in the mean basal ganglia metabolite ratios between patients and controls. Psychometric performance improved in 50 % of patients with minimal HE following LOLA, but no significant changes were observed in brain volumes, cerebral magnetization transfer ratios, the diffusion weighted imaging variables or the cerebral metabolite ratios. MR variables, as applied in this study, do not identify patients with minimal HE, nor do they reflect changes in psychometric performance following LOLA.

Sepsis and toxic shock syndrome4 justified large doses of clindamycin to inhibit t-xotoxin protein synthesis,15 and immunoglobulin acted to neutralise exotoxins and superantigens.2,3 Nonsteroidal anti-inflammatory drugs were avoided-they can adversely impair immune responses or mask symptoms and delay diagnosis. Early clinical suspicion, aggressive antimicrobial therapy, and the early multidisciplinary involvement of senior team members facilitate optimum management.